arXiv subjects

P. N. Timonin

Publications and source records attributed to P. N. Timonin.

At least 19 recordsLinked to original sources

arXiv2022

Disentanglement, disorder lines, and Majorana edge states in a solvable quantum chain

We study the exactly solvable 1D model: the dimerized $XY$ chain with uniform and staggered transverse fields, equivalent upon fermionization to the noninteracting dimerized Kitaev-Majorana chain with modulation. The model has three known gapped phases with local and nonlocal (string) orders, along with the gapless incommensurate (IC) phase in the $U(1)$ limit. The criticality is controlled by the properties of zeros of model's partition function, analytically continued onto the complex wave numbers. In the ground state they become complex zeros of the spectrum of the Hamiltonian. The analysis of those roots yields the phase diagram which contains continuous quantum phase transitions and weaker singularities known as disorder lines (DLs) or modulation transitions. The latter, reported for the first time in this model, are shown to occur in two types: DLs of the first kind with continuous appearance of the IC oscillations, and DLs of the second kind corresponding to a jump of the wave number of oscillations. The salient property of zeros of the spectrum is that the ground state is shown to be separable (factorized) and the model is disentangled on a subset of the DLs. From analysis of those zeros we also find the Majorana edge states and their wave functions.

cond-mat.str-el↗

arXiv2021

Disorder lines, modulation, and partition function zeros in free fermion models

The modulation is analyzed from the analytical properties of zeros of free fermionic partition function on the complex plane of wave numbers. It is shown how these properties are related to the oscillations of correlation functions. This approach can be used for analysis of phase transitions with local or nonlocal order parameters, as well as for the disorder lines. We find an infinite cascade of disorder lines at finite temperature in the quantum $XY$ chain (equivalent to free fermions). The well-known ground state factorization on the disorder line, and consequently, disentanglement, is shown to follow directly from analytical properties of this model on the complex plane. From the quantum-classical correspondence the results for the chain are used to detect the disorder lines in several frustrated 2D Ising models. The present formalism can be applied to other fermionic models in two and three spatial dimensions. In particular, we find the temperature-dependent Fermi wave vector of oscillations in the degenerate gas of 3D fermions, which naturally leads in the limit $T \to 0$ to the definition of the Fermi energy as the surface of quantum criticality. The modulation is a very common phenomenon, and it occurs in a large variety of models. The important point is that all these modulation transitions can be related to the complex zeros of partition functions, as done in the present study.

cond-mat.str-el↗

arXiv2020

Statistics of geometric clusters in Potts model: statistical mechanics approach

The percolation of Potts spins with equal values in Potts model on graphs (networks) is considered. The general method for finding the Potts clusters size distributions is developed. It allows for full description of percolation transition when giant cluster of equal-valued Potts spins appears. The method is applied to the short-ranged q-state ferromagnetic Potts model on the Bethe lattices with the arbitrary coordination number z. The analytical results for the field-temperature percolation phase diagram of geometric spin clusters and their size distribution are obtained. The last appears to be proportional to that of the classical non-correlated bond percolation with the bond probability, which depends on temperature and Potts model parameters.

cond-mat.stat-mech↗

arXiv2019

String and conventional order parameters in the solvable modulated quantum chain

The phase diagram and the order parameters of the exactly solvable quantum 1D model are analysed. The model in its spin representation is the dimerized XY spin chain in the presence of uniform and staggered transverse fields. In the fermionic representation this model is the dimerized non-interacting Kitaev chain with a modulated chemical potential. The model has a rich phase diagram which contains phases with local and non-local (string) orders. We have calculated within the same systematic framework the local order parameters (spontaneous magnetization) and the non-local string order parameters, along with the topological winding numbers for all domains of the phase diagram. The topologically nontrivial phase is shown to have a peculiar oscillating string order with the wavenumber $q=π/2$, awaiting for its experimental confirmation.

cond-mat.stat-mech↗

arXiv2019

Statistics of geometric clusters in the Ising model on a Bethe lattice: statistical mechanics approach

The statistical mechanics method is developed for determination of generating function of like-sign spin clusters' size distribution in Ising model as modification of Ising-Potts model by K. K. Murata (1979). It is applied to the ferromagnetic Ising model on Bethe lattice. The analytical results for the field-temperature percolation phase diagram of + spin clusters and their size distribution are obtained. The last appears to be proportional to that of the classical non-correlated bond percolation with the bond probability, which depends on temperature and Ising model parameters.

cond-mat.stat-mech↗

arXiv2018

Statistical mechanics of high-density bond percolation

High-density (HD) percolation describes the percolation over specific $κ$ -clusters, which are the compact sets of sites each connected to $κ$ nearest filled sites at least. It takes place in the classical patterns of independently distributed sites or bonds in which the ordinary percolation transition also exsists. Hence, the study of series of $κ$ -type percolations amounts to the description of structure of classical clusters for which $κ$ -clusters constitute $κ$ -cores nested one into another. Such data are needed for description of a number of physical, biological information and other properties of complex systems on random lattices, graphs and networks. They range from magnetic properties of semiconductor alloys to anomalies in supercooled water and clustering in biological and social networks. Here we present the statistical mechanics approach to study HD bond percolation on arbitrary graph. It is shown that generating function for $κ$ -clusters' size distribution can be obtained from partition function of specific $q$-state Potts-Ising model in $q \to 1$ limit. Using this approach we find exact $κ$ -clusters' size distribution for Bethe lattice and Erdos Renyi graph. The application of the method to Euclidean lattices is also discussed.

cond-mat.stat-mech↗

arXiv2017

Infinite cascades of phase transitions in the classical Ising chain

We report the new exact results on one of the best studied models in statistical physics: the classical antiferromagnetic Ising chain in a magnetic field. We show that the model possesses an infinite cascade of thermal phase transitions (also known as "disorder lines" or geometric phase transitions). The phase transition is signalled by a change of asymptotic behavior of the nonlocal string-string correlation functions when their monotonous decay becomes modulated by incommensurate oscillations. The transitions occur for rarefied ($m$-periodic) strings with arbitrary odd $m$. We propose a duality transformation which maps the Ising chain onto the $m$-leg Ising tube with nearest-neighbor couplings along the legs and the plaquette four-spin interactions of adjacent legs. Then the $m$-string correlation functions of the Ising chain are mapped onto the two-point spin-spin correlation functions along the legs of the $m$-leg tube. We trace the origin of these cascades of phase transitions to the lines of the Lee-Yang zeros of the Ising chain in $m$-periodic complex magnetic field, allowing us to relate these zeros to the observable (and potentially measurable) quantities.

cond-mat.stat-mech↗

arXiv2017

Clusters' size-degree distribution for bond percolation

To address some physical properties of percolating systems it can be useful to know the degree distributions in finite clusters along with their size distribution. Here we show that to achieve this aim for classical bond percolation one can use the $q \to 1$ limit of suitably modified q-state Potts model. We consider a version of such model with the additional complex variables and show that its partition function gives generating function for the size and degree distribution in this limit. We derive this distribution analytically for bond percolation on Bethe lattice and complete graph. The possibility to expand the applications of present method to other clusters' characteristics and to models of correlated percolation is discussed.

cond-mat.stat-mech↗

arXiv2015

Exploring Percolative Landscapes: Infinite Cascades of Geometric Phase Transitions

The evolution of many kinetic processes in 1+1 (space-time) dimensions results in 2d directed percolative landscapes. The active phases of these models possess numerous hidden geometric orders characterized by various types of large-scale and/or coarse-grained percolative backbones that we define. For the patterns originated in the classical directed percolation (DP) and contact process (CP) we show from the Monte-Carlo simulation data that these percolative backbones emerge at specific critical points as a result of continuous phase transitions. These geometric transitions belong to the DP universality class and their nonlocal order parameters are the capacities of corresponding backbones. The multitude of conceivable percolative backbones implies the existence of infinite cascades of such geometric transitions in the kinetic processes considered. We present simple arguments to support the conjecture that such cascades of transitions is a generic feature of percolation as well as many others transitions with nonlocal order parameters.

cond-mat.stat-mech↗

arXiv2015

Thermodynamics of dilute XX chain in a field

The isotropic spin one-half XY chain in transverse field (XX chain) has specific ground state phase with permanent criticality (quasi-long-range ordered, QLRO, phase) which exists in a field less than nearest-neighbor exchange. It is characterized by gapless excitations and power law decay of transverse correlators. The dilution of XX chain has drastic effect on this phase: the infinite series of quantum phase transitions marked by magnetization jumps appears in it. The thermodynamics of dilute XX chain allows exact analytical description revealing the peculiarities of the appearing transitions. We calculate the low-temperature magnetization, entropy, longitudinal magnetic susceptibility and specific heat of dilute model to elucidate the influence of quantum transitions on their field and low-temperature behavior. The changes of pair spin correlators under dilution are also analyzed. We argue that other dilute quantum spin chains and ladders with the gapless (algebraic) spin-liquid states would also exhibit the quantum jumps under variation of couplings and field similar to those of XX chain.

cond-mat.stat-mech↗

arXiv2015

Hidden percolation transition in kinetic replication process

The one-dimensional kinetic contact process with parallel update is introduced and studied by the mean-field approximation and Monte Carlo (MC) simulations. Contrary to a more conventional scenario with single active phase for 1d models with Ising-like variables, we find two different adjacent active phases in the parameter space of the proposed model with a second-order transition between them and a multiphase point where the active and the absorbing phases meet. While one of the active phases is quite standard with a smooth average filling of the space-time lattice, the second active phase demonstrates a very subtle (hidden) percolating order which becomes manifest only after certain transformation from the original model. We determine the percolation order parameter for active-active phase transition and discuss such hidden orders in other low-dimensional systems. Our MC data demonstrate finite-size critical and near-critical scaling of the order parameter relaxation for the two phase transitions. We find three independent critical indices for them and conclude that they both belong to the directed percolation universality class.

cond-mat.stat-mech↗

arXiv2013

Field-induced inhomogeneous ground states of antiferromagnetic ANNNI chains

Finite-size effects are studied in ground states of antiferromagnetic (AF) ANNNI chains in a field. It is shown that field can induce a variety of inhomogeneous states in finite chains. They are composed of two shifted AF states with the kink at their junction and are highly degenerate with respect to the kink position. The phase diagram field-exchange ratio for finite chains is presented.

cond-mat.stat-mech↗

arXiv2013

Ferrimagnetism of dilute Ising antiferromagnets

It is shown that nearest-neighbor antiferromagnetic interactions of identical Ising spins on imbalanced bipartite lattice and imbalanced bipartite hierarchical fractal result in ferrimagnetic order instead of antiferromagnetic one. On some crystal lattices dilute Ising antiferromagnets may also become ferrimagnets due to the imbalanced nature of the magnetic percolation cluster when it coexists with the percolation cluster of vacancies. As evidenced by the existing experiments on $Fe_pZn_{1-p}F_2$, such ferrimagnetism is inherent property of bcc lattice so thermodynamics of these compounds at low $p$ can be similar to that of antiferromagnet on imbalanced hierarchical fractal.

cond-mat.dis-nn↗

arXiv2012

Smeared spin-flop transition in random antiferromagnetic Ising chain

At T = 0 and a sufficiently large field, the nearest-neighbor antiferromagnetic Ising chain undergoes a first-order spin-flop transition into the ferromagnetic phase. We consider its smearing under the random-bond disorder such that all independent random bonds are antiferromagnetic (AF). It is shown that it can be described exactly for arbitrary distribution of AF bonds P(J). Moreover, the site magnetizations of finite chains can be found analytically in this model. We consider continuous P(J) which is zero above some -J_1 and behaves near it as (-J_1 - J)^λ, λ> -1. In this case ferromagnetic phase emerges continuously in a field H > H_c = 2J_1. At 0 > λ> -1 it has usual second-order anomalies near H_c with critical indices obeying the scaling relation and depending on λ. At λ> 0 the higher-order transitions appear (third, fourth etc.) marked by the divergence of corresponding nonlinear susceptibilities. In the chains with even number of spins the intermediate "bow-tie" phase with linearly modulated AF order exists between AF and ferromagnetic ones at J_1 < H < H_c. Its origin can be traced to the infinite correlation length of the degenerate AF phase from which it emerges. This implies the existence of similar inhomogeneous phases with size- and form-dependent order in a number of other systems with infinite correlation length. The possibility to observe the signs of "bow-tie" phase in low-T neutron diffraction experiments is discussed.

cond-mat.dis-nn↗

arXiv2011

Spin ice in a field: quasi-phases and pseudo-transitions

Thermodynamics of the short-range model of spin ice magnets in a field is considered in the Bethe - Peierls approximation. The results obtained for [111], [100] and [011] fields agrees reasonably well with the existing Monte-Carlo simulations and some experiments. In this approximation all extremely sharp field-induced anomalies are described by the analytical functions of temperature and applied field. In spite of the absence of true phase transitions the analysis of the entropy and specific heat reliefs over H-T plane allows to discern the "pseudo-phases" with specific character of spin fluctuations and define the lines of more or less sharp "pseudo-transitions" between them.

cond-mat.mtrl-sci↗

arXiv2010

Hysteresis loop signatures of phase transitions in a mean-field model of disordered Ising magnet

In accordance with recent experiments the mean-field type theories predict the presence of numerous metastable minima (states) in the rugged free-energy landscape of frustrated disordered magnets. This multiplicity of long-lived states with lifetimes greater than $10^5 s$ makes the task to experimentally determine which of them has the lowest free energy (and thus what thermodynamic phase the sample is in) seem rather hopeless the more so as we do not know a protocol (such as field-cooling or zero-field-cooling) leading to the equilibrium state(s). Nevertheless here we show in the framework of Landau-type phenomenological model that signatures of the mean-field equilibrium phase transitions in such highly nonequilibrium systems may be found in the evolution of the hysteresis loop form. Thus the sequence of transitions from spin-glass to mixed phase and to ferromagnetic one results in the changes from inclined hysteresis loop to that with the developing vertical sides and to one with the perfectly vertical sides. Such relation between loop form and the location of global minimum may hold beyond the mean-field approximation and can be useful in the real experiments and Monte-Carlo simulations of the problems involving rugged potential landscape. Also the very existence of the quasi-static loops in spin glass and mixed phases implies that the known disorder-smoothing of the first-order transition can be always accompanied by the emergence of multiple metastable states.

cond-mat.dis-nn↗

arXiv2010

Thermodynamics of strongly frustrated magnet in a field: Ising antiferromagnet on triangular Husimi lattice

Some strongly frustrated magnets such as the "spin-ice" compounds fail to produce any magnetic order at finite temperatures even in the presence of magnetic field. Still they have very unusual low-temperature thermodynamic properties related to the field-induced ground state transitions. Here we show that general qualitative picture of such peculiar thermodynamics can be obtained in the antiferromagnetic Ising model on the triangular Husimi lattice. The analytical results for this model show magnetic plateaus, entropy spikes, crossing points and peculiarities in magnetic susceptibility and specific heat behavior reflecting the existence of ground state transitions. These signatures of strong frustration may help in search of new frustrated magnets and in the interpretation of experimental data.

cond-mat.mtrl-sci↗

arXiv2010

Dipole-glass concept and history-dependent phenomena in relaxors

The possibility to explain basic physical properties of relaxors within the concept of the dipole-glass transition is discussed. We argue that this concept provides the only consistent picture accounting of all known anomalous features of relaxors. The origin of their history-dependent properties can be naturally traced to the main paradigm of glass-state theory - the existence of numerous metastable states. Based on this paradigm phenomenological description of known history-dependent phenomena in relaxors agrees qualitatively with experiments.

cond-mat.mtrl-sci↗