The role of long relaxation times in a simple model with massless modes

Abstract

The next-nearest-neighbour Ising model with competing nearest-neighbour (nn) and next-nearest-neighbour (nnn) interactions, provides an example of a system in which massless modes destroy order at any finite temperature. This occurs only at a critical ratio, Kc, of the nnn and nn interactions. In this paper we investigate the role of long relaxation times in determining the behaviour of the system when the ratio of the nnn and nn interactions, K, is at and close to this critical ratio. Despite the absence of an order–disorder transition in systems with K = Kc, in Monte Carlo simulations reported here the temperature-dependent behaviour of the relaxation times indicates the existence of a glass transition with a glass transition temperature of Tg ≈ 0.26 in a model with nn interaction J = kB = 1.

Tensor network simulation for the frustrated $J_1$-$J_2$ Ising model on the square lattice

“…However, the physical quantities can not go to the convegence with the kept bond dimension D increasing. There exist a few research about g = 0.5 supporting finite phase transition temperature [42][43][44], but the most claim that the critical temperature is suppressed to zero temperature due to the high degeneracy, just like one-dimensional system [9,11,15,20,21,24]. We put g = 0.5, T c = 0 in the phase diagram.…”

Numerical transfer matrix study of frustrated next-nearest-neighbor Ising models on square lattices

“…For κ < 1/2, it has generally been assumed that the transition is part of the Ising universality class, but recent cluster mean-field approximation and effective-field theory study suggest that a narrow first-order transition regime might also be found at κ < ∼ 1/2 [16,17]. Several simulation studies further suggest a nonzero transition temperature at κ = 1/2 proper, i.e., T c (κ = 1/2) > 0 [18,31,32], in marked contrast to prior works [11,[33][34][35][36]. Because theoretical approximations behave irregularly around κ < ∼ 1/2 [37], however, a conclusive assessment has thus far remained out of reach.…”