arXiv subjects

A. O. Sorokin

Publications and source records attributed to A. O. Sorokin.

15 recordsLinked to original sources

arXiv2022

Phase transition in the three-dimensional $O(N)\otimes O(M)$ model: a Monte Carlo study

Using Monte Carlo simulations, we consider the lattice version of the $O(N)\otimes O(M)$ sigma model for $2\leq M\leq4$ and $M\leq N \leq8$. We find a continuous transition for $N\geq M+4$. Estimates of the critical exponents for cases of second-order and weak first-order transitions are found. For $M=2$ our estimates of the exponents and marginal dimensionality $N_c^+(M)$ are in good agreement with the results of the non-perturbative renormalization group approach. For $M\geq2$ we find estimates of the exponents and marginal dimensionality between the values obtained in the first and second orders of the large-N expansion. To complete the picture, we also consider the usual $O(N)$ model ($M=1$).

hep-lat↗

arXiv2021

First-order transition in the stacked-$J_1$-$J_2$ Ising model on a cubic lattice

We investigate critical properties of the stacked-$J_1$-$J_2$ Ising model on a cubic lattice. Using Monte Carlo simulations and renormalization group, we find a single phase transition of the first order for $J_2/J_1>1/2$. The renormgroup approach predicts that a transition can be of the second order from the universality class of the $O(2)$ model, but the Monte Carlo results show another set of critical exponents: exponents continuously vary form the values typical for a first-order transition in the finite-size scaling theory at $1/2<J_2/J_1<1$ to the Ising values in the limit $J_2/J_1\to\infty$. We also exclude the pseudo-first-order behavior observed in the $J_1$-$J_2$ Ising model on a square lattice for $0.67\lesssim J_2/J_1\lesssim0.9$.

cond-mat.str-el↗

arXiv2021

First-order and pseudo-first-order transition in the high dimensional $O(N)\otimes O(M)$ model

Using the renormalization group approach, we consider the $O(N)\otimes O(M)$ model in four and more dimensions. We find that independently on $N$ and $M$, for $N\geq M\geq 2$, a transition can be of both the first and second order. In $d>4$, we also cannot exclude a pseudo-first-order behavior. As specific physically interesting cases, we consider the lattice version of the $O(2)\otimes O(2)$, $O(3)\otimes O(2)$ and $O(3)\otimes O(3)$ sigma models on a four dimensional hypercubic lattice. In all these cases, we find a distinct first-order transition.

cond-mat.str-el↗

arXiv2021

Triple helix vs. skyrmion lattice in two-dimensional non-centrosymmetric magnets

It is commonly assumed that a lattice of skyrmions, emerging in two-dimensional non-centrosymmetric magnets in external magnetic fields, can be represented as a sum of three magnetic helices. In order to test this assumption we compare two approaches to a description of regular skyrmion structure. We construct (i) a lattice of Belavin-Polyakov-like skyrmions within the stereographic projection method, and (ii) a deformed triple helix defined with the use of elliptic functions. The estimates for the energy density and magnetic profiles show that these two ansatzes are nearly identical at zero temperature for intermediate magnetic fields. However at higher magnetic fields, near the transition to topologically trivial uniform phase, the stereographic projection method is preferable, particularly, for the description of disordered skyrmion liquid phase. We suggest to explore the intensities of the secondary Bragg peaks to obtain the additional information about the magnetic profile of individual skyrmions. We estimate these intensities to be several percents of the main Bragg peak at high magnetic fields.

cond-mat.str-el↗

arXiv2018

Critical and multicritical behavior in the Ising-Heisenberg universality class

Critical behavior of three-dimensional classical frustrated antiferromagnets with a collinear spin ordering and with an additional twofold degeneracy of the ground state is studied. We consider two lattice models, whose continuous limit describes a single phase transition with a symmetry class differing from the class of non-frustrated magnets as well as from the classes of magnets with non-collinear spin ordering. A symmetry breaking is described by a pair of independent order parameters, which are similar to order parameters of the Ising and O(N) models correspondingly. Using the renormalization group method, it is shown that a transition is of first order for non-Ising spins. For Ising spins, a second order phase transition from the universality class of the O(2) model may be observed. The lattice models are considered by Monte Carlo simulations based on the Wang-Landau algorithm. The models are a ferromagnet on a body-centered cubic lattice with the additional antiferromagnetic exchange interaction between next-nearest-neighbor spins and an antiferromagnet on a simple cubic lattice with the additional interaction in layers. We consider the cases N=1,2,3 and in all of them find a first-order transition. For the N=1 case we exclude possibilities of the second order or pseudo-first order of a transition. An almost second order transition for large N is also discussed.

cond-mat.str-el↗

arXiv2018

Towards an effective theory of skyrmion crystals

We consider multiskyrmion configurations in 2D ferromagnets with Dzyaloshinskii-Moriya (DM) interaction and the magnetic field, using the stereographic projection method. In the absence of DM interaction, $D$, and the field, $B$, the skyrmions do not interact and the exact multiskyrmion solution is a sum of individual projections. In certain range of $B, D\neq0$, skyrmions become stable and form a hexagonal lattice. The shape of one skyrmion on the plane is fully determined by $D$ and $B$. We describe multiskyrmion configurations by simple sums of individual skyrmion projections, of the same shape and adjusted scale. This procedure reveals pairwise and triple interactions between skyrmions, and the energy of proposed hexagonal structure is found in a good agreement with previous studies. It allows an effective theory of skyrmion structures in terms of variables, referring to individual skyrmions, i.e., their position, size and phase, elliptic distortions etc.

cond-mat.str-el↗

arXiv2018

Topological defects and critical phenomena in two-dimensional frustrated helimagnets

Using a simple model of a frustrated helimagnet, the critical behavior is numerically investigated for planar or isotropic spins, and for cases of one or two chiral order parameters. The helical structure in this model arises from the competition between exchange interactions of spins of the first two range orders in one direction (in both directions) of a square lattice. The main result is that the critical and temperature behavior is primarily determined by topological defects that are present in all cases. In the case of planar spins, vortices, fractional vortices and domain walls are present in the system. Their interaction leads to the appearance of the phase of a chiral spin liquid, or induces a single first-order transition, and in the vicinity of the Lifshitz point vortices lead to a reentrant phase transition to the phase with a collinear quasi-long-range order. When transitions in the chiral and continuous order parameters are separated in temperature, they are of the 2D Ising and Kosterlitz-Thouless types correspondingly. In the case of isotropic spins, so-called $\mathbb{Z}_2$ vortices are present. They do not lead to the appearance of a phase with long-range or quasi-long-range order in the case of one chiral order parameter. However, their interaction leads to a sharp change in the temperature dependence of the correlation length (crossover). In the case of two chiral parameters, there are long-range chiral order of the Ising type (chiral spin liquid) and domain walls. However, as a result of the interaction of vortices and walls, the crossover and chiral transition occur at the same temperature as a first-order transition.

cond-mat.str-el↗

arXiv2018

Interaction of domain walls and vortices in the two-dimensional O(2) and O(3) principal chiral models

Using extensive Monte Carlo simulations, we investigate the critical properties of domain walls, vortices and $\mathbb{Z}_2$ vortices in the Ising-$O(2)$ and Ising-$O(3)\otimes O(2)$ models. We have consider the nontrivial case when disorder in the Ising order parameter induces disorder in the continuous parameter. Such a situation arises when a domain wall becomes opaque for continuous parameter correlations. We find that in this case the vortex density at the BKT transition (or crossover) point turns out to be non-universal, while the wall density at the Ising transition remains universal, i.e. in agreement with the Ising model. An important part of this study is the numerical measurement of defect-defect correlators. We find that the wall-vortex correlator tends to zero in the thermodynamic limit at the Ising point, which explains the universality of the wall density. A possible multicritical behavior of the models is also discussed.

cond-mat.str-el↗

arXiv2018

Critical density of topological defects upon a continuous phase transition

Using extensive Monte Carlo simulations, we test the hypothesis that the density of corresponding topological defects has an universal value at the temperature of a continuous phase transition. We consider several simple two-dimensional models where domain walls, vortices, so-called $\mathbb{Z}_2$ vortices or their combinations are presented. These topological defects are relevant correspondingly to an Ising second-order phase transition, a Berezinskii-Kosterlitz Thouless transition and an explicit crossover. We compare results for square and triangular lattices as well as for the complicated situation when two types of defects are presented and two transitions occur separated in temperature. All considered cases demonstrate consentient results confirming the hypothesis.

cond-mat.str-el↗

arXiv2016

First order transition induced by topological defects in the O(3) principal chiral model

Using Monte Carlo simulations, we study thermal and critical properties of two systems, in which domain walls and so-called $Z_2$-vortices as topological defects are presented. The main model is a lattice version of the $O(3)$ principal chiral model. We find a first order transition and give qualitative arguments that the first order is induced by topological defects. We also consider the model of frustrated antiferromagnet on a square lattice with the additional exchange interaction between spins of the third range order. This model belongs to the same symmetry class. In this model, a transition is of first order too.

cond-mat.other↗

arXiv2016

Determination of CFT central charge by the Wang-Landau algorithm

We propose a simple method to estimate the central charge of the conformal field theory corresponding to a critical point of a two-dimensional lattice model from Monte Carlo simulations. The main idea is to use the Wang-Landau flat-histogram algorithm, which allows us to obtain the free energy of a lattice model on a torus as a function of torus radii. The central charge is calculated with a good precision from a free energy scaling at the critical point. We apply the method to the Ising, tricritical Ising (Blume-Capel), Potts and site-diluted Ising models, and also discuss estimation of conformal weights.

cond-mat.stat-mech↗

arXiv2016

Numerical determination of the CFT central charge in the site-diluted Ising model

We propose a new numerical method to determine the central charge of the conformal field theory models corresponding to the 2D lattice models. In this method, the free energy of the lattice model on the torus is calculated by the Wang-Landau algorithm and then the central charge is obtained from a free energy scaling with respect to the torus radii. The method is applied for determination of the central charge in the site-diluted Ising model.

cond-mat.stat-mech↗

arXiv2015

Magnon spectrum in ferromagnets with a skyrmion

The analysis of the spin wave excitations in two-dimensional isotropic Heisenberg ferromagnet is performed with a single skyrmion in the ground state. We employ the ideas of semiclassical quantization method, duly modified for the use of the lattice model and Maleyev-Dyson boson representation of spin operators. The resulting Schrödinger equation for magnons describes the dispersion and wave functions of spin-wave excitations with strictly non-negative spectrum. In contrast to usual ferromagnet, we demonstrate the existence of three zero modes, corresponding to conformal symmetries spontaneously violated by the skyrmion configuration.

cond-mat.str-el↗

arXiv2014

Ising-XY Transition in Three-dimensional Frustrated Antiferromagnets with Collinear Ordering

Using Monte Carlo simulations, we study the critical behavior of two models of frustrated XY antiferromagnets with a collinear spin ordering and with an additional twofold degeneracy of the ground state. We consider a classic antiferromagnet on a body-centered cubic lattice with an additional antiferromagnetic exchange interaction between next-nearest spins, and a ferromagnet with an extra antiferromagnetic intralayer exchange. In both models, a single first-order transition on the discrete and continuous order parameters is found. Observed critical pseudo-exponents are in agreement with exponents of XY magnets with a planar spin ordering like a stacked-triangular antiferromagnet and helimagnets belonging to the same symmetry class.

cond-mat.str-el↗

arXiv2012

Chiral Spin Liquid in two-dimensional XY Helimagnets

We carry out Monte-Carlo simulations to discuss critical properties of a classical two-dimensional XY frustrated helimagnet on a square lattice. We find two successive phase transitions upon the temperature decreasing: the first one is associated with breaking of a discrete Z_2 symmetry and the second one is of the Berezinskii-Kosterlitz-Thouless (BKT) type at which the SO(2) symmetry breaks. Thus, a narrow region exists on the phase diagram between lines of the Ising and the BKT transitions that corresponds to a chiral spin liquid.

cond-mat.str-el↗