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

Abstract

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.

Monte Carlo renormalization group of dilute 3D Ising dynamics

“…[12,13]. A refined RG analysis of the problem has shown the stability of the critical behavior of weakly disordered three dimensional systems with respect to the replica symmetry breaking effects [14]. All obtained results confirm the existence of a new universal class of the critical behavior, which is formed by diluted Ising-like systems.…”

Short-time dynamics and critical behavior of the three-dimensional site-diluted Ising model

“…[12,13]. A refined RG analysis of the problem has shown the stability of the critical behavior of weakly disordered three-dimensional * Electronic address: prudnikp@univer.omsk.su systems with respect to the replica symmetry breaking effects [14]. All obtained results confirm the existence of a new universal class of the critical behavior, which is formed by diluted Ising-like systems.…”

“…The statistical errors for exponents are estimated by dividing all data into five data sets. On the base of these values of exponents and average value of ω/z, we determine the final values of the critical exponents z = 2.185 (25), β/ν = 0.533 (13), ν = 0.668 (14), β = 0.356 (6), and ω = 0.369(96) for p = 0.95, and z = 2.208(32), β/ν = 0.508 (17), ν = 0.685 (21), β = 0.348 (11), and ω = 0.404(110) for p = 0.8. In this part of the paper, we present the numerical investigations of the short-time critical dynamics of the 3D site-diluted Ising model on the lattice with linear size L = 128, starting from a disordered state with small initial magnetizations m 0 = 0.01, 0.02, and 0.03 for samples with spin concentration p = 0.8 only.…”

Critical behavior of the two-dimensional Ising model with long-range correlated disorder

“…[34] using bosonization of the 2D massive Thirring model [55]. The latter allows one to eliminate the terms in action (65) which are diagonal in replicas and local in space by means of the identity Λ π cos √ 4πϕ(r)…”