arXiv subjects

Peter C. W. Holdsworth

Publications and source records attributed to Peter C. W. Holdsworth.

At least 19 recordsLinked to original sources

arXiv2022

Violation of the fluctuation-dissipation theorem and effective temperatures in spin ice

We present numerical tests of the fluctuation-dissipation theorem (FDT) in the dumbbell model of spin ice with parameters suitable for dysprosium titanate. The tests are made for local spin variables, magnetic monopole density, and energy. We are able to achieve local equilibrium in which the FDT is satisfied down to $T=0.4$ K below which the system completely freezes. Non-equilibrium dynamics, together with violation of the FDT, are nonetheless observed following a thermal quench into the non-contractable monopole pair regime. Despite FDT violation, an approximate linear response regime allows for the identification of effective non-equilibrium temperatures which are different for each variable. The spin variable appears hotter than the heat reservoir, the monopole concentration responds with a lower effective temperature while the energy has a negative effective temperature. Results are discussed in the context of the monopole picture of spin ice and compared to the structure of FDT violations in other glassy materials. Prospectives for future experiments are reviewed.

cond-mat.stat-mech↗

arXiv2021

Electric field fluctuations in the two-dimensional Coulomb fluid

The structure factor for electric field correlations in the two dimensional Coulomb fluid is simulated and compared to theories of the dielectric function. Singular changes in the structure factor occur at the BKT insulator to conductor transition, as well as at a higher temperature correlation transition between a poor electrolyte and perturbed Debye-Hückel fluid. Structure factors are found to differ in the canonical and grand canonical ensembles, with the poor electrolyte showing full ensemble inequivalence. We identify mechanisms of `underscreening' and `pinch point' scattering that are relevant to experiments on ionic liquids and artificial spin ice respectively.

cond-mat.stat-mech↗

arXiv2020

The effect of driving on model C interfaces

We consider the effect of uniform driving on the interface between two phases which are described by model C dynamics. The non-driven system has a classical Gaussian interface described by capillary wave theory. The model under driving retains Gaussian statistics but the interface statistics are modified by driving, notably the height fluctuations are suppressed and the correlation length of the fluctuations is increased. The model we introduce can also be used as a model for the effect of activity on interface dynamics.

cond-mat.stat-mech↗

arXiv2018

Emergent Electrochemistry in Spin Ice: Debye-Hückel Theory and Beyond

The low-temperature picture of dipolar spin ice in terms of the Coulomb fluid of its fractionalised magnetic monopole excitations has allowed analytic and conceptual progress far beyond its original microscopic spin description. Here we develop its thermodynamic treatment as a `magnetolyte', a fluid of singly and doubly charged monopoles, an analogue of the electrochemical system ${\rm 2 H_2O = H_3O^+ +OH^- = H_4O^{2+} + O^{2-}}$, but with perfect symmetry between oppositely charged ions. For this lattice magnetolyte, we present an analysis based on Debye-Hückel theory, which is accurate at all temperatures and incorporates `Dirac strings' imposed by the microscopic ice rule constraints at the level of Pauling's approximation. Our results are in close agreement with the specific heat from numerical simulations as well as new experimental measurements with an improved lattice correction, which we present here, on the spin ice materials $\mathrm{Ho_2Ti_2O_7}$ and $\mathrm{Dy_2Ti_2O_7}$. Our study of the magnetolyte shows how electrochemistry can emerge in non-electrical systems. We also provide new experimental tests of Debye-Hückel theory and its extensions. The application of our results also yields insights into the electrochemical behaviour of water ice and liquid water, which are closely related to the spin ice magnetolyte.

cond-mat.str-el↗

arXiv2017

An electric-field representation of the harmonic XY model

The two-dimensional harmonic XY (HXY) model is a spin model in which the classical spins interact via a piecewise parabolic potential. We argue that the HXY model should be regarded as the canonical classical lattice spin model of phase fluctuations in two-dimensional condensates, as it is the simplest model that guarantees the modular symmetry of the experimental systems. Here we formulate a lattice electric-field representation of the HXY model and contrast this with an analogous representation of the Villain model and the two-dimensional Coulomb gas with a purely rotational auxiliary field. We find that the HXY model is a spin-model analogue of a lattice electric-field model of the Coulomb gas with an auxiliary field, but with a temperature-dependent vacuum (electric) permittivity that encodes the coupling of the spin vortices to their background spin-wave medium. The spin vortices map to the Coulomb charges, while the spin-wave fluctuations correspond to auxiliary-field fluctuations. The coupling explains the striking differences in the high-temperature asymptotes of the specific heats of the HXY model and the Coulomb gas with an auxiliary field. Our results elucidate the propagation of effective long-range interactions throughout the HXY model (whose interactions are purely local) by the lattice electric fields. They also imply that global spin-twist excitations (topological-sector fluctuations) generated by local spin dynamics are ergodically excluded in the low-temperature phase. We discuss the relevance of these results to condensate physics.

cond-mat.stat-mech↗

arXiv2016

Topological-sector fluctuations and ergodicity breaking at the Berezinskii-Kosterlitz-Thouless transition

The Berezinskii-Kosterlitz-Thouless (BKT) phase transition drives the unbinding of topological defects in many two-dimensional systems. In the two-dimensional Coulomb gas, it corresponds to an insulator-conductor transition driven by charge deconfinement. We investigate the global topological properties of this transition, both analytically and by numerical simulation, using a lattice-field description of the two-dimensional Coulomb gas on a torus. The BKT transition is shown to be an ergodicity breaking between the topological sectors of the electric field, which implies a definition of topological order in terms of broken ergodicity. The breakdown of local topological order at the BKT transition leads to the excitation of global topological defects in the electric field, corresponding to different topological sectors. The quantized nature of these classical excitations, and their strict suppression by ergodicity breaking in the low-temperature phase, afford striking global signatures of topological-sector fluctuations at the BKT transition. We discuss how these signatures could be detected in experiments on, for example, magnetic films and cold-atom systems.

cond-mat.stat-mech↗

arXiv2016

Critical Casimir forces from the equation of state of quantum critical systems

The mapping between a classical length and inverse temperature as imaginary time provides a direct equivalence between the Casimir force of a classical system in $D$ dimensions and internal energy of a quantum system in $d$$=$$D$$-$$1$ dimensions. The scaling functions of the critical Casimir force of the classical system with periodic boundaries thus emerge from the analysis of the symmetry related quantum critical point. We show that both non-perturbative renormalization group and quantum Monte Carlo analysis of quantum critical points provide quantitative estimates for the critical Casimir force in the corresponding classical model, giving access to widely different aspect ratios for the geometry of confined systems. In the light of these results we propose protocols for the experimental realization of critical Casimir forces for periodic boundaries through state-of-the-art cold-atom and solid-state experiments.

cond-mat.stat-mech↗

arXiv2016

Direct calculation of the critical Casimir force in a binary fluid

We show that critical Casimir effects can be accessed through direct simulation of a model binary fluid passing through the demixing transition. We work in the semi grand canonical ensemble, in slab geometry, in which the Casimir force appears as the excess of the generalized pressure, $P_{\bot}-nμ$. The excesses of the perpendicular pressure, $P_{\bot}$, and of $nμ$, are individually of much larger amplitude. A critical pressure anisotropy is observed between forces parallel and perpendicular to the confinement direction, which collapses onto a universal scaling function closely related to that of the critical Casimir force.

cond-mat.stat-mech↗

arXiv2016

From quantum to thermal topological-sector fluctuations of strongly interacting bosons in a ring lattice

Inspired by recent experiments on Bose-Einstein condensates in ring traps, we investigate the topological properties of the phase of a one-dimensional Bose field in the presence of both thermal and quantum fluctuations -- the latter ones being tuned by the depth of an optical lattice applied along the ring. In the regime of large filling of the lattice, quantum Monte Carlo simulations give direct access to the full statistics of fluctuations of the Bose-field phase, and of its winding number $W$ along the ring. At zero temperature the winding-number (or topological-sector) fluctuations are driven by quantum phase slips localized around a Josephson link between two lattice wells, and their { susceptibility} is found to jump at the superfluid-Mott insulator transition. At finite (but low) temperature, on the other hand, the winding number fluctuations are driven by thermal activation of nearly uniform phase twists, whose activation rate is governed by the superfluid fraction. A quantum-to-thermal crossover in winding number fluctuations is therefore exhibited by the system, and it is characterized by a conformational change in the topologically non-trivial configurations, from localized to uniform phase twists, which can be experimentally observed in ultracold Bose gases via matter-wave interference.

cond-mat.quant-gas↗

arXiv2015

Finite-size scaling of the magnetization probability density for the critical Ising model in slab geometry

The magnetization probability density in d=2 and 3 dimensional Ising models in slab geometry of volume $L_{\parallel}^{d-1} \times L_{\perp}$ is computed through Monte-Carlo simulation at the critical temperature and zero magnetic field. The finite-size scaling of this distribution and its dependence on the system aspect-ratio $ρ=\frac{L_{\perp}}{L_{\parallel}}$ and boundary conditions is discussed. In the limiting case $ρ\to 0$ of a macroscopically large slab ($L_{\parallel} \gg L_{\perp}$) the distribution is found to scale as a Gaussian function for all tested system sizes and boundary conditions.

cond-mat.stat-mech↗

arXiv2015

Phase order in superfluid helium films

Classic experimental data on helium films are transformed to estimate a finite-size phase order parameter that measures the thermal degradation of the condensate fraction in the two-dimensional superfluid. The order parameter is found to evolve thermally with the exponent $β= 3 π^2/128$, a characteristic, in analogous magnetic systems, of the Berezinskii-Kosterlitz-Thouless (BKT) phase transition. Universal scaling near the BKT fixed point generates a collapse of experimental data on helium and ferromagnetic films, and implies new experiments and theoretical protocols to explore the phase order. These results give a striking example of experimental finite-size scaling in a critical system that is broadly relevant to two-dimensional Bose fluids.

cond-mat.stat-mech↗

arXiv2014

AC Wien effect in spin ice, manifest in non-linear non-equilibrium susceptibility

We predict the non-linear non-equilibrium response of a "magnetolyte", the Coulomb fluid of magnetic monopoles in spin ice. This involves an increase of the monopole density due to the second Wien effect---a universal and robust enhancement for Coulomb systems in an external field---which in turn speeds up the magnetization dynamics, manifest in a non-linear susceptibility. Along the way, we gain new insights into the AC version of the classic Wien effect. One striking discovery is that of a frequency window where the Wien effect for magnetolyte and electrolyte are indistinguishable, with the former exhibiting perfect symmetry between the charges. In addition, we find a new low-frequency regime where the growing magnetization counteracts the Wien effect. We discuss for what parameters best to observe the AC Wien effect in Dy$_2$Ti$_2$O$_7$.

cond-mat.stat-mech↗

arXiv2014

Critical Casimir forces in a magnetic system: An experimental protocol

We numerically test an experimentally realizable method for the extraction of the critical Casimir force based on its thermodynamic definition as the derivative of the excess free energy with respect to system size. Free energy differences are estimated for different system sizes by integrating the order parameter along an isotherm. The method could be developed for experiments on magnetic systems and could give access to the critical Casimir force for any universality class. By choosing an applied field that opposes magnetic ordering at the boundaries, the Casimir force is found to increase by an order of magnitude over zero-field results.

cond-mat.stat-mech↗

arXiv2014

Magnetic-Moment Fragmentation and Monopole Crystallization

The Coulomb phase, with its dipolar correlations and pinch-point-scattering patterns, is central to discussions of geometrically frustrated systems, from water ice to binary and mixed-valence alloys, as well as numerous examples of frustrated magnets. The emergent Coulomb phase of lattice-based systems has been associated with divergence-free fields and the absence of long-range order. Here, we go beyond this paradigm, demonstrating that a Coulomb phase can emerge naturally as a persistent fluctuating background in an otherwise ordered system. To explain this behavior, we introduce the concept of the fragmentation of the field of magnetic moments into two parts, one giving rise to a magnetic monopole crystal, the other a magnetic fluid with all the characteristics of an emergent Coulomb phase. Our theory is backed up by numerical simulations, and we discuss its importance with regard to the interpretation of a number of experimental results.

cond-mat.stat-mech↗

arXiv2013

Onsager's Wien Effect on a Lattice

The Second Wien Effect describes the non-linear, non-equilibrium response of a weak electrolyte in moderate to high electric fields. Onsager's 1934 electrodiffusion theory along with various extensions has been invoked for systems and phenomena as diverse as solar cells, surfactant solutions, water splitting reactions, dielectric liquids, electrohydrodynamic flow, water and ice physics, electrical double layers, non-Ohmic conduction in semiconductors and oxide glasses, biochemical nerve response and magnetic monopoles in spin ice. In view of this technological importance and the experimental ubiquity of such phenomena, it is surprising that Onsager's Wien effect has never been studied by numerical simulation. Here we present simulations of a lattice Coulomb gas, treating the widely applicable case of a double equilibrium for free charge generation. We obtain detailed characterisation of the Wien effect and confirm the accuracy of the analytical theories as regards the field evolution of the free charge density and correlations. We also demonstrate that simulations can uncover further corrections, such as how the field-dependent conductivity may be influenced by details of microscopic dynamics. We conclude that lattice simulation offers a powerful means by which to investigate system-specific corrections to the Onsager theory, and thus constitutes a valuable tool for detailed theoretical studies of the numerous practical applications of the Second Wien Effect.

cond-mat.mtrl-sci↗

arXiv2013

Dissipation induced non-Gaussian energy fluctuations

The influence of dissipation on the fluctuation statistics of the total energy is investigated through both a phenomenological and a stochastic model for dissipative energy-transfer through a cascade of states. In equilibrium the states obey equipartition and the total energy obeys the central limit theorem, giving Gaussian fluctuations. In the presence of dissipation, the fluctuations can be driven non-Gaussian if there is macroscopic energy transfer from large to small scales. We are thus able to equate the non-Gaussian order parameter fluctuations in model equilibrium systems at criticality with energy fluctuations in these dissipative systems. Energy fluctuations in the phenomenological model map directly onto the 1/f^alpha noise problem and numerical simulations of the stochastic model yield results in qualitative agreement with these predictions.

cond-mat.stat-mech↗

arXiv2012

Topological Sector Fluctuations and Curie Law Crossover in Spin Ice

At low temperatures, a spin ice enters a Coulomb phase - a state with algebraic correlations and topologically constrained spin configurations. In Ho2Ti2O7, we have observed experimentally that this process is accompanied by a non-standard temperature evolution of the wave vector dependent magnetic susceptibility, as measured by neutron scattering. Analytical and numerical approaches reveal signatures of a crossover between two Curie laws, one characterizing the high temperature paramagnetic regime, and the other the low temperature topologically constrained regime, which we call the spin liquid Curie law. The theory is shown to be in excellent agreement with neutron scattering experiments. On a more general footing, i) the existence of two Curie laws appears to be a general property of the emergent gauge field for a classical spin liquid, and ii) sheds light on the experimental difficulty of measuring a precise Curie-Weiss temperature in frustrated materials; iii) the mapping between gauge and spin degrees of freedom means that the susceptibility at finite wave vector can be used as a local probe of fluctuations among topological sectors.

cond-mat.stat-mech↗

arXiv2012

Spin-wave analysis of the transverse-field Ising model on the checkerboard lattice

The ground state properties of the S=1/2 transverse-field Ising model on the checkerboard lattice are studied using linear spin wave theory. We consider the general case of different couplings between nearest neighbors (J1) and next-to-nearest neighbors (J2). In zero field the system displays a large degeneracy of the ground state, which is exponential in the system size (for J1=J2) or in the system's linear dimensions (for J2>J1). Quantum fluctuations induced by a transverse field are found to be unable to lift this degeneracy in favor of a classically ordered state at the harmonic level. This remarkable fact suggests that a quantum-disordered ground state can be instead promoted when non-linear fluctuations are accounted for, in agreement with existing results for the isotropic case J1=J2. Moreover spin-wave theory shows sizable regions of instability which are further candidates for quantum-disordered behavior.

cond-mat.str-el↗