arXiv subjects

Thomas Vojta

Publications and source records attributed to Thomas Vojta.

At least 19 recordsLinked to original sources

arXiv2026

Interwoven long-range order induced by random fields

We propose a distinct type of long-range ordered phase that can occur in classical and quantum many-particle systems. It is induced by impurities and defects that locally break a subset of the order-parameter symmetries, i.e., by random-field disorder that couples to a composite vestigial order parameter. The proposed ``implectic'' phase is characterized by spontaneous symmetry breaking on the background of the spatially interwoven domain structure created by the random fields. We explicitly demonstrate the existence of this phase in a layered $J_1-J_2$ Ising magnet by means of large-scale Monte Carlo simulations. We then discuss numerous potential applications in systems featuring charge and spin density wave order including frustrated magnets, cuprate and iron-based superconductors, and ultracold atoms.

cond-mat.dis-nn↗

arXiv2026

Mean-field theory of myopic self-avoiding fractional Brownian motion

Myopic self-avoiding fractional Brownian motion (FBM) is a stochastic process in which an ensemble of particles is driven by fractional Gaussian noise while being repelled by the gradient of the time-integrated ensemble density [J. House, R. Bakhshizada, S. Janu\v{s}onis, R. Metzler, and T. Vojta, Phys. Rev. E 112, 034119 (2025)]. Depending on the anomalous diffusion exponent $\alpha$ characterizing the noise, the process features two dynamical regimes: an interaction-dominated regime ($\alpha < \alpha_c=4/(d+2)$) where the mean-density interaction governs long-time dynamics, and a noise-dominated regime ($\alpha > \alpha_c$) where FBM correlations prevail. In the interaction-dominated regime, the mean-squared displacement grows as $\langle r^2(t) \rangle \sim t^{4/(d+2)}$ regardless of $\alpha$, while for $\alpha > \alpha_c$ the standard FBM scaling $\langle r^2(t) \rangle \sim t^{\alpha}$ is recovered. Here, we develop an analytical mean-field theory of myopic self-avoiding FBM, based on a Fokker-Planck approach to the interaction-dominated regime. This allows us to derive closed-form polynomial solutions for the probability density. To compare with computer simulations, we develop an efficient radial binning algorithm that significantly reduces the computational complexity, making large-scale three-dimensional simulations feasible. Extensive simulations in one, two, and three dimensions confirm the analytical predictions. We also discuss the application of the process to the self-organization of serotonergic axons (fibers) in vertebrate brains, where FBM paths with self-avoidance provide a natural framework for understanding spatial heterogeneities of fiber densities.

cond-mat.stat-mech↗

arXiv2026

Diffusion disorder in the contact process

We study the effects of spatially inhomogeneous diffusion on the non-equilibrium phase transition in the contact process. The directed-percolation critical point in the contact process is known to be stable against the addition of a spatially uniform diffusion term. Correspondingly, we find quenched randomness in the diffusion rates to be irrelevant by power counting in the field-theory of the contact process. However, large-scale Monte Carlo simulations demonstrate that such diffusion disorder destabilizes the clean directed percolation critical point. Instead, the transition belongs to the same infinite-randomness universality class as the contact process with disorder in the infection or healing rates. To explain these results, we develop an effective model with an infinite diffusion rate; it shows that diffusion disorder generates an effective disorder in the healing rates. The same mechanism also appears in the field-theoretic description: Whereas diffusion disorder is irrelevant by power-counting, it generates standard random-mass disorder under renormalization. We discuss the validity of this mechanism for other absorbing state transitions and non-equilibrium phase transitions in general.

cond-mat.stat-mech↗

arXiv2025

Quantum critical behavior of diluted quasi-one-dimensional Ising chains

CoNb$_2$O$_6$ is a unique magnetic material. It features bulk three-dimensional magnetic order at low temperatures, but its quantum critical behavior in a magnetic field is well described by the one-dimensional transverse-field Ising universality class. This behavior is facilitated by the structural arrangement of magnetic Co$^{2+}$ ions in nearly isolated zig-zag chains. In this work, we investigate the effect of random site dilution on the critical properties of such a quasi-one-dimensional quantum Ising system. To this end, we introduce an anisotropic site-diluted three-dimensional transverse-field Ising model. We find that site dilution leads to unconventional activated scaling behavior at the quantum phase transition. Interestingly, the critical exponents of the quantum critical point are in good agreement with those of the disordered three-dimensional transverse-field Ising universality class, despite the strong spatial anisotropy. We discuss the generality our findings as well as implications for experiments.

cond-mat.str-el↗

arXiv2025

Magnetic field-tuned magnetic order and metamagnetic criticality in non-stoichiometric CeAuBi$_2$

We present a detailed study of magnetization, resistivity, heat capacity, and X-ray and neutron powder diffraction measurements performed on single crystals of non-stoichiometric CeAuBi$_2$, Au deficiency 18$\%$, a strongly correlated antiferromagnet with N\'eel temperature T$_N$ = 13.2 K. Field-dependent magnetization measurements reveal a large magnetic anisotropy at low temperatures with an easy axis along the crystallographic c-axis, in which direction a spin-flop transition exhibits strong features in magnetization, specific heat, and resistivity at H$_c$ = 75 kOe. The constructed temperature-field phase diagram connects this transition to the suppression of magnetic order, which evolves from a second-order nature into a first-order transition that bifurcates at the spin-flop into three transitions below 1 K. The smoothed nature of the metamagnetic transitions in non-stoichiometric CeAuBi$_2$ is well described by an Ising model with weak quenched disorder, suggesting that the presence of Au vacancies is sufficient to smear the complex metamagnetic behavior and tune the critical behavior of magnetic order.

cond-mat.str-el↗

arXiv2025

Amplitude mode at the superfluid-insulator transition on a random lattice

We study the superfluid-insulator quantum phase transition of interacting bosons by means of large-scale Monte Carlo simulations in the presence of both topological and generic quenched disorders. Recent work has demonstrated that the amplitude mode at this transition broadens and localizes in the presence of dilution disorder, whereas it remains a well-defined delocalized excitation for topological (connectivity) disorder. Here, we analyze the crossover between systems with purely topological disorder and systems with additional bond randomness to disentangle the roles that disorder and interactions play for amplitude mode localization. Specifically, we analyze the scalar susceptibility and its spectral density on both sides of the quantum phase transition. We also discuss the implications of our results for the potential observation of amplitude mode localization in experiments.

cond-mat.quant-gas↗

arXiv2025

Fractional Brownian motion with mean-density interaction: a myopic self-avoiding fractional stochastic process

Fractional Brownian motion is a Gaussian stochastic process with long-range correlations in time; it has been shown to be a useful model of anomalous diffusion. Here, we investigate the effects of mutual interactions in an ensemble of particles undergoing fractional Brownian motion. Specifically, we introduce a mean-density interaction in which each particle in the ensemble is coupled to the gradient of the total, time-integrated density produced by the entire ensemble. We report the results of extensive computer simulations for the mean-squared displacements and the probability densities of particles undergoing one-dimensional fractional Brownian motion with such a mean-density interaction. We find two qualitatively different regimes, depending on the anomalous diffusion exponent $\alpha$ characterizing the fractional Gaussian noise. The motion is governed by the interactions for $\alpha < 4/3$ whereas it is dominated by the fractional Gaussian noise for $\alpha > 4/3$. We develop a scaling theory explaining our findings. We also discuss generalizations to higher space dimensions and nonlinear interactions, the relation of our process to the ``true'' or myopic self-avoiding walk, as well as applications to the growth of strongly stochastic axons (e.g., serotonergic fibers) in vertebrate brains.

cond-mat.stat-mech↗

arXiv2024

Phases and Phase Transitions of the Disordered Quantum Clock Model

We study the phases and phase transitions of a disordered one-dimensional quantum $q$-state clock Hamiltonian using large-scale Monte Carlo simulations. Making contact with earlier results, we confirm that the clean, translational invariant version of the model, for $q=6$, hosts an intermediate emergent quasi-long-range ordered (QLRO) phase between the symmetry-broken true long-range ordered (TLRO) phase and the disordered (paramagnetic) phase. With increasing disorder strength, the quasi-long-range ordered phase shrinks and finally vanishes at a multi-critical point, beyond which there is a direct transition from the TLRO phase to the paramagnetic phase. After establishing the phase diagram, we characterize the critical behaviors of the various quantum phase transitions in the model. We find that weak disorder is an irrelevant perturbation of the Berezinskii-Kosterlitz-Thouless transitions that separate the QLRO phase from the TLRO and paramagnetic phases. For stronger disorder, some of the critical exponents become disorder-dependent already before the system reaches the multicritical point. We also show that beyond the multicritical point, the direct transition from the TLRO phase to the paramagnetic phase is governed by an infinite-randomness critical point in line with strong-disorder renormalization group predictions. While our numerical results are for $q=6$, we expect the qualitative features of the behavior to hold for all $q>4$.

cond-mat.dis-nn↗

arXiv2024

Magnetic properties of diluted hexaferrites

We revisit the magnetic properties of the hexagonal ferrite PbFe$_{12-x}$Ga$_x$O$_{19}$. Recent experiments have reported puzzling dependencies of the ordering temperature and the saturation magnetization on the Ga concentration $x$. To explain these observations, we perform large-scale Monte Carlo simulations, focusing on the effects of an unequal distribution of the Ga impurities over the five distinct Fe sublattices. Ab-initio density-functional calculations predict that the Ga ions preferably occupy the $12k$ sublattice and (to a lesser extent) the $2a$ sublattice. We incorporate this insight into a nonuniform model of the Ga distribution. Monte Carlo simulations using this model lead to an excellent agreement between the theoretical and experimental values of the ordering temperature and saturation magnetization, indicating that the unequal distribution of the Ga impurities is the main reason for the unusual magnetic properties of PbFe$_{12-x}$Ga$_x$O$_{19}$. We also compute the temperature and concentration dependencies of the sublattice magnetizations, and we study the character of the zero-temperature transition that takes place when the ordering temperature is tuned to zero.

cond-mat.dis-nn↗

arXiv2024

Scalar susceptibility of a diluted classical XY model

We analyze the amplitude fluctuations in a diluted 3D classical XY model near the magnetic phase transition, motivated by the unusual localization properties of the amplitude (Higgs) mode recently found at the disordered superfluid-Mott glass quantum phase transition. We calculate the amplitude correlation function and the corresponding scalar susceptibility by means of Monte Carlo simulations. In contrast to the quantum case, in which the scalar susceptibility was found to violate naive scaling, we find that the scalar susceptibility of the classical system fulfills naive scaling (employing the clean critical exponents, as expected from the Harris criterion) as the temperature is varied across the phase transition for several dilutions. We discuss possible reasons for this discrepancy as well as the generality of our findings.

cond-mat.dis-nn↗

arXiv2024

Critical Behavior and Collective Modes at the Superfluid Transition in Amorphous Systems

We investigate the critical behavior and the dynamics of the amplitude (Higgs) mode close to the superfluid-insulator quantum phase transition in an amorphous system (i.e., a system subject to topological randomness). In particular, we map the two-dimensional Bose-Hubbard Hamiltonian defined on a random Voronoi-Delaunay lattice onto a (2+1)-dimensional layered classical XY model with correlated topological disorder. We study the resulting model by laying recourse to classical Monte Carlo simulations. We specifically focus on the scalar susceptibility of the order parameter to study the dynamics of the amplitude mode. To do so, we harness the maximum entropy method to perform the analytic continuation of the scalar susceptibility to real frequencies. Our analysis shows that the amplitude mode remains delocalized in the presence of such topological disorder, quite at odds with its behavior in generic disordered systems, where the randomness localizes the Higgs mode. Furthermore, we show that the critical behavior of the topologically disordered system is identical to that of its translationally invariant counterpart, consistent with a modified Harris criterion. This suggests that the localization of the collective excitations in the presence of disorder is tied to the critical behavior of the quantum phase transition rather than a simple Anderson-localization-type interference mechanism.

cond-mat.dis-nn↗

arXiv2023

Helicity modulus and chiral symmetry breaking for boundary conditions with finite twist

We study the response of a two-dimensional classical XY model to a finite (non-infinitesimal) twist of the boundary conditions. We use Monte Carlo simulations to evaluate the free energy difference between periodic and twisted-periodic boundary conditions and find deviations from the expected quadratic dependence on the twist angle. Consequently, the helicity modulus (spin-stiffness) shows a non-trivial dependence on the twist angle. We show that the deviation from the expected behavior arises because of the mixing of states with opposite chirality which leads to an additional entropy contribution in the quasi-long-range ordered phase. We give an improved prescription for the numerical evaluation of the helicity modulus for a finite twist, and we discuss the spontaneous breaking of the chiral symmetry for the anti-periodic boundary conditions. We also discuss applications to discrete spin systems and some experimental scenarios where boundary conditions with finite twist are necessary.

cond-mat.stat-mech↗

arXiv2023

Memory-multi-fractional Brownian motion with continuous correlations

We propose a generalization of the widely used fractional Brownian motion (FBM), memory-multi-FBM (MMFBM), to describe viscoelastic or persistent anomalous diffusion with time-dependent memory exponent $α(t)$ in a changing environment. In MMFBM the built-in, long-range memory is continuously modulated by $α(t)$. We derive the essential statistical properties of MMFBM such as response function, mean-squared displacement (MSD), autocovariance function, and Gaussian distribution. In contrast to existing forms of FBM with time-varying memory exponents but reset memory structure, the instantaneous dynamic of MMFBM is influenced by the process history, e.g., we show that after a step-like change of $α(t)$ the scaling exponent of the MSD after the $α$-step may be determined by the value of $α(t)$ before the change. MMFBM is a versatile and useful process for correlated physical systems with non-equilibrium initial conditions in a changing environment.

cond-mat.stat-mech↗

arXiv2022

Contact process with simultaneous spatial and temporal disorder

We study the absorbing-state phase transition in the one-dimensional contact process under the combined influence of spatial and temporal random disorders. We focus on situations in which the spatial and temporal disorders decouple. Couched in the language of epidemic spreading, this means that some spatial regions are, at all times, more favorable than others for infections, and some time periods are more favorable than others independent of spatial location. We employ a generalized Harris criterion to discuss the stability of the directed percolation universality class against such disorder. We then perform large-scale Monte Carlo simulations to analyze the critical behavior in detail. We also discuss how the Griffiths singularities that accompany the nonequilibrium phase transition are affected by the simultaneous presence of both disorders.

cond-mat.stat-mech↗

arXiv2022

Novel Emergent Phases in a Two-Dimensional Superconductor

In this letter, we report our observation of an extraordinarily rich phase diagram of a LaScO$_3$/SrTiO$_3$ heterostructure. Close to the superconducting transition temperature, the system hosts a superconducting critical point of the Infinite-randomness type characterized by an effective dynamical exponent $\nu z$ that diverges logarithmically. At lower temperatures, we find the emergence of a magnetic field-tuned metallic phase that co-exists with a quantum Griffiths phase (QGP). Our study reveals a previously unobserved phenomenon in 2D superconductors -- an unanticipated suppression of the QGP below a crossover temperature in this system. This concealment is accompanied by the destruction of the superconducting quantum critical point signaled by a power-law divergence (in temperature) of the effective dynamical exponent. These observations are entirely at odds with the predictions of the infinite-randomness scenario and challenge the very concept of a vanishing energy scale associated with a quantum critical point. We develop and discuss possible scenarios like smearing of the phase transition that could plausibly explain our observations. Our findings challenge the notion that QGP is the ultimate ground state in two-dimensional superconductors.

cond-mat.supr-con↗

arXiv2022

Stripe order, impurities, and symmetry breaking in a diluted frustrated magnet

We investigate the behavior of the frustrated $J_1$-$J_2$ Ising model on a square lattice under the influence of random dilution and spatial anisotropies. Spinless impurities generate a random-field type disorder for the spin-density wave (stripe) order parameter. These random fields destroy the long-range stripe order in the case of spatially isotropic interactions. Combining symmetry arguments, percolation theory and large-scale Monte Carlo simulations, we demonstrate that arbitrarily weak spatial interaction anisotropies restore the stripe phase. More specifically, the transition temperature $T_c$ into the stripe phase depends on the interaction anisotropy $ΔJ$ via $T_c \sim 1/|\ln (ΔJ)|$ for small $ΔJ$. This logarithmic dependence implies that very weak anisotropies are sufficient to restore the transition temperature to values comparable to that of the undiluted system. We analyze the critical behavior of the emerging transition and find it to belong to the disordered two-dimensional Ising universality class, which features the clean Ising critical exponents and universal logarithmic corrections. We also discuss the generality of our results and their consequences for experiments.

cond-mat.dis-nn↗

arXiv2021

Inhomogeneous mean-field approach to collective excitations in disordered interacting bosons

We develop an inhomogeneous quantum mean-field approach to the behavior of collective excitations across the superfluid-Mott glass quantum phase transition in two dimensions, complementing recent quantum Monte Carlo simulations [Phys. Rev. Lett. {\bf 125}, 027002 (2020)]. In quadratic (Gaussian) approximation, the Goldstone (phase) and Higgs (amplitude) modes completely decouple. Each is described by a disordered Bogoliubov Hamiltonian which can be solved by an inhomogeneous multi-mode Bogoliubov transformation. We find that the Higgs mode is spatially localized in both phases. The corresponding scalar spectral function shows a broad peak that is noncritical in the sense that its peak frequency does not soften but remains nonzero across the quantum phase transition. In contrast, the lowest-energy Goldstone mode delocalizes in the superfluid phase, leading to a zero-frequency spectral peak. We compare these findings to the results of the quantum Monte Carlo simulations. We also relate them to general results on the localization of bosonic excitations, and we discuss the limits and generality of our approach.

cond-mat.str-el↗

arXiv2021

Random-strain-induced correlations in materials with intertwined nematic and magnetic orders

Electronic nematicity is rarely observed as an isolated instability of a correlated electron system. Instead, in iron pnictides and in certain cuprates and heavy-fermion materials, nematicity is intertwined with an underlying spin-stripe or charge-stripe state. As a result, random strain, ubiquitous in any real crystal, creates both random-field disorder for the nematic degrees of freedom and random-bond disorder for the spin or charge ones. Here, we put forward an Ashkin-Teller model with random Baxter fields to capture the dual role of random strain in nematic systems for which nematicity is a composite order arising from a stripe state. Using Monte Carlo to simulate this $\textit{random Baxter-field model}$, we find not only the expected break-up of the system into nematic domains, but also the emergence of nontrivial disorder-promoted magnetic correlations. Such correlations enhance and tie up the fluctuations associated with the two degenerate magnetic stripe states from which nematicity arises, leaving characteristic signatures in the spatial profile of the magnetic domains, in the configurational space of the spin variables, and in the magnetic noise spectrum. We discuss possible experimental manifestations of these effects in iron-pnictide superconductors. Our work establishes the random Baxter-field model as a more complete alternative to the random-field Ising model to describe complex electronic nematic phenomena in the presence of disorder.

cond-mat.str-el↗