Strong-disorder paramagnetic-ferromagnetic fixed point in the square-lattice +- J Ising model

TL;DR

This study reveals a strong-disorder fixed point governing the paramagnetic-ferromagnetic transition in the square-lattice +- J Ising model at low temperatures, with distinct critical exponents from the pure Ising model.

Contribution

It identifies a new strong-disorder fixed point controlling the transition at low T, different from the pure Ising fixed point, supported by finite-size scaling Monte Carlo analysis.

Findings

Transition line is reentrant for T<T*

Transitions are continuous and governed by a strong-disorder fixed point

Critical exponents differ from the pure Ising model

Abstract

We consider the random-bond +- J Ising model on a square lattice as a function of the temperature T and of the disorder parameter p (p=1 corresponds to the pure Ising model). We investigate the critical behavior along the paramagnetic-ferromagnetic transition line at low temperatures, below the temperature of the multicritical Nishimori point at T*= 0.9527(1), p*=0.89083(3). We present finite-size scaling analyses of Monte Carlo results at two temperature values, T=0.645 and T=0.5. The results show that the paramagnetic-ferromagnetic transition line is reentrant for T<T*, that the transitions are continuous and controlled by a strong-disorder fixed point with critical exponents nu=1.50(4) and eta=0.128(8), and beta = 0.095(5). This fixed point is definitely different from the Ising fixed point controlling the paramagnetic-ferromagnetic transitions for T>T*. Our results for the critical exponents are consistent with the hyperscaling relation 2 beta/nu - eta = d - 2 = 0.