Ground-state magnetization of the Ising spin glass: A recursive numerical method and Chen-Ma scaling

TL;DR

This paper introduces a recursive numerical method and analytical theory to study the ground-state magnetization of quasi-one-dimensional Ising spin glasses, revealing unique magnetic behaviors and exponents differing from 1D systems.

Contribution

The paper develops an exact recursive numerical approach and extends the Chen-Ma scaling argument to analyze Q1D Ising spin glasses, providing new insights into their magnetic properties.

Findings

Magnetization exhibits a power-law divergence with a unique spectrum of magnetic exponents.

The magnetic exponent transitions from distribution-dependent to a constant value.

Analytical formula for the magnetic exponent matches numerical results.

Abstract

The ground-state properties of quasi-one-dimensional (Q1D) Ising spin glass are investigated using an exact numerical approach and analytical arguments. A set of coupled recursive equations for the ground-state energy are introduced and solved numerically. For various types of coupling distribution, we obtain accurate results for magnetization, particularly in the presence of a weak external magnetic field. We show that in the weak magnetic field limit, similar to the 1D model, magnetization exhibits a singular power-law behavior with divergent susceptibility. Remarkably, the spectrum of magnetic exponents is markedly different from that of the 1D system even in the case of two coupled chains. The magnetic exponent makes a crossover from being dependent on the distribution function to a constant value independent of distribution. We provide an analytic theory for these observations by extending the Chen-Ma argument to the Q1D case. We derive an analytical formula for the exponent which is in perfect agreement with the numerical results.