Numerical Study of Competing Spin-Glass and Ferromagnetic Order

TL;DR

This study uses zero-temperature domain-wall renormalization group analysis to explore the phase behavior of 2D and 3D random Ising models with Gaussian couplings, revealing distinct flow regimes and fixed points.

Contribution

It provides a detailed numerical analysis of phase transitions in random Ising models, identifying fixed points and phase boundaries without evidence of an additional phase.

Findings

DWRG trajectories collapse on two curves in the ($J_0,J$) plane.

Flows toward ferromagnetic fixed point for high $J_0/J$ ratios.

Flows toward paramagnetic or spin-glass fixed points for low $J_0/J$ ratios.

Abstract

Two and three dimensional random Ising models with a Gaussian distribution of couplings with variance $J$ and non-vanishing mean value $J_0$ are studied using the zero-temperature domain-wall renormalization group (DWRG). The DWRG trajectories in the ($J_0,J$) plane after rescaling can be collapsed on two curves: one for $J_0/J > r_c$ and other for $J_0/J < r_c$. In the first case the DWRG flows are toward the ferromagnetic fixed point both in two and three dimensions while in the second case flows are towards a paramagnetic fixed point and spin-glass fixed point in two and three dimensions respectively. No evidence for an extra phase is found.