Magnetization-resolved density of states and quasi-first order transition in the two-dimensional random bond Ising model: an entropic sampling study

TL;DR

This study employs an entropy sampling method to analyze the phase transitions and density of states in the two-dimensional random-bond Ising model, revealing a quasi-first order transition at zero temperature and reentrant phase boundary behavior.

Contribution

The paper introduces an efficient entropy sampling scheme for low-energy states and applies it to uncover the nature of phase transitions in the 2D random-bond Ising model, including a quasi-first order transition.

Findings

Reentrant phase boundary below the multicritical point.

Evidence of a quasi-first order transition at zero temperature.

Finite-size scaling supports $eta=0$ and $ u=1.50(8)$.

Abstract

Systems with quenched disorder possess complex energy landscapes that are challenging to explore under the conventional Monte Carlo method. In this work, we implement an efficient entropy sampling scheme for accurate computation of the entropy function in low-energy regions. The method is applied to the two-dimensional $\pm J$ random-bond Ising model, where frustration is controlled by the fraction $p$ of ferromagnetic bonds. We investigate the low-temperature paramagnetic--ferromagnetic phase boundary below the multicritical point at $T_N = 0.9530(4)$, $P_N = 0.89078(8)$, as well as the zero-temperature ferromagnetic--spin-glass transition. Finite-size scaling analysis reveals that the phase boundary for $T < T_N$ exhibits reentrant behavior. By analyzing the evolution of the magnetization-resolved density of states $g(E, M)$ and ground-state spin configurations against increasing frustration, we provide strong evidence that the zero-temperature transition is quasi-first order. Finite-size scaling conducted on the spin-glass side supports the validity of $\beta = 0$, with a correlation length exponent $\nu = 1.50(8)$. Our results provide new insights into the nature of the ferromagnetic-to-spin-glass phase transition in an extensively degenerate ground state.