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P. V. Prudnikov

Publications and source records attributed to P. V. Prudnikov.

8 recordsLinked to original sources
arXiv2017

Universal Berezinskii-Kosterlitz-Thouless dynamic scaling in the intermediate timerange in frustrated Heisenberg antiferromagnets on triangular lattice

We investigate non-equilibrium properties of the frustrated Heisenberg antiferromagnets on the triangular lattice. Nonequilibrium critical relaxation of frustrated Heisenberg antiferromagnets shows a dynamic transition (or, at least, sharp crossover) at the same temperature $T_{\rm u}=0.282 J$ as for static properties due to unbinding of $\mathbb{Z}_2$-vortices. We show that starting from the high-temperature initial state, due to presence of $\mathbb{Z}_2$-vortices in the considering system, in a broad temperature range $T<T_{\rm u}$ the dynamic properties in the intermediate time range are similar to those of two-dimensional XY model below Berezinskii-Kosterlitz-Thouless transition. The interaction of $\mathbb{Z}_2$-vortices with spin-wave degrees of freedom does not emerge until rather long times.

cond-mat.str-el↗
arXiv2010

Renormalization-group description of nonequilibrium critical short-time relaxation processes: a three-loop approximation

The influence of nonequilibrium initial values of the order parameter on its evolution at a critical point is described using a renormalization group approach of the field theory. The dynamic critical exponent $θ'$ of the short time evolution of a system with an $n$-component order parameter is calculated within a dynamical dissipative model using the method of $\varepsilon$-expansion in a three-loop approximation. Numerical values of $θ'$ for three-dimensional systems are determined using the Padé-Borel method for the summation of asymptotic series.

cond-mat.stat-mech↗
arXiv2009

The influence of long-range correlated defects on critical ultrasound propagation in solids

The effect of long-range correlated quenched structural defects on the critical ultrasound attenuation and sound velocity dispersion is studied for three-dimensional Ising-like systems. A field-theoretical description of the dynamic critical effects of ultrasound propagation in solids is performed with allowance for both fluctuation and relaxation attenuation mechanisms. The temperature and frequency dependences of the dynamical scaling functions of the ultrasound critical characteristics are calculated in a two-loop approximation for different values of the correlation parameter $a$ of the Weinrib-Halperin model with long-range correlated defects. The asymptotic behavior of the dynamical scaling functions in hydrodynamic and critical regions is separated. The influence of long-range correlated disorder on the asymptotic behavior of the critical ultrasonic anomalies is discussed.

cond-mat.dis-nn↗
arXiv2005

Boundary critical behaviour at m-axial Lifshitz points of semi-infinite systems with a surface plane perpendicular to a modulation axis

Semi-infinite $d$-dimensional systems with an $m$-axial bulk Lifshitz point are considered whose ($d-1$)-dimensional surface hyper-plane is oriented perpendicular to one of the $m$ modulation axes. An $n$-component $ϕ^4$ field theory describing the bulk and boundary critical behaviour when (i) the Hamiltonian can be taken to have O(n) symmetry and (ii) spatial anisotropies breaking its Euclidean symmetry in the $m$-dimensional coordinate subspace of potential modulation directions may be ignored is investigated. The long-distance behaviour at the ordinary surface transition is mapped onto a field theory with the boundary conditions that both the order parameter $\bmϕ$ and its normal derivative $\partial_n\bmϕ$ vanish at the surface plane. The boundary-operator expansion is utilized to study the short-distance behaviour of $\bmϕ$ near the surface. Its leading contribution is found to be controlled by the boundary operator $\partial_n^2\bmϕ$. The field theory is renormalized for dimensions $d$ below the upper critical dimension $d^*(m)=4+m/2$, with a corresponding surface source term $\propto \partial_n^2\bmϕ$ added. The anomalous dimension of this boundary operator is computed to first order in $ε=d^*-d$. The result is used in conjunction with scaling laws to estimate the value of the single independent surface critical exponent $β_{\mathrm{L}1}^{(\mathrm{ord},\perp)}$ for $d=3$. Our estimate for the case $m=n=1$ of a uniaxial Lifshitz point in Ising systems is in reasonable agreement with published Monte Carlo results.

cond-mat.stat-mech↗
arXiv2005

Critical sound attenuation in a diluted Ising system

The field-theoretic description of dynamical critical effects of the influence of disorder on acoustic anomalies near the temperature of the second-order phase transition is considered for three-dimensional Ising-like systems. Calculations of the sound attenuation in pure and dilute Ising-like systems near the critical point are presented. The dynamical scaling function for the critical attenuation coefficient is calculated. The influence of quenched disorder on the asymptotic behaviour of the critical ultrasonic anomalies is discussed.

cond-mat.dis-nn↗
arXiv2003

Critical behavior of disordered systems with replica symmetry breaking

A field-theoretic description of the critical behavior of weakly disordered systems with a $p$-component order parameter is given. For systems of an arbitrary dimension in the range from three to four, a renormalization group analysis of the effective replica Hamiltonian of the model with an interaction potential without replica symmetry is given in the two-loop approximation. For the case of the one-step replica symmetry breaking, fixed points of the renormalization group equations are found using the Pade-Borel summing technique. For every value $p$, the threshold dimensions of the system that separate the regions of different types of the critical behavior are found by analyzing those fixed points. Specific features of the critical behavior determined by the replica symmetry breaking are described. The results are compared with those obtained by the $ε$-expansion and the scope of the method applicability is determined.

cond-mat.dis-nn↗
arXiv2001

Stability of critical behaviour of weakly disordered systems with respect to the replica symmetry breaking

A field-theoretic description of the critical behaviour of the weakly disordered systems is given. Directly, for three- and two-dimensional systems a renormalization analysis of the effective Hamiltonian of model with replica symmetry breaking (RSB) potentials is carried out in the two-loop approximation. For case with 1-step RSB the fixed points (FP's) corresponding to stability of the various types of critical behaviour are identified with the use of the Pade-Borel summation technique. Analysis of FP's has shown a stability of the critical behaviour of the weakly disordered systems with respect to RSB effects and realization of former scenario of disorder influence on critical behaviour.

cond-mat.dis-nn↗