Finite Size Scaling Analysis of Exact Ground States for +/-J Spin Glass Models in Two Dimensions

TL;DR

This study uses polynomial algorithms to analyze the zero-temperature ground states of 2D +/-J spin glass models, revealing a critical bond concentration where ferromagnetic and spin glass orders vanish, with finite size scaling describing the behavior.

Contribution

It introduces a finite size scaling analysis of exact ground states for 2D +/-J spin glass models, identifying a unique critical concentration and characterizing the stability of magnetic orders.

Findings

Existence of a critical bond concentration p_c where magnetic orders vanish.

Finite size scaling form describes domain wall energy near p_c.

Stiffness exponent is slightly negative, indicating no intermediate spin glass phase.

Abstract

With the help of EXACT ground states obtained by a polynomial algorithm we compute the domain wall energy at zero-temperature for the bond-random and the site-random Ising spin glass model in two dimensions. We find that in both models the stability of the ferromagnetic AND the spin glass order ceases to exist at a UNIQUE concentration p_c for the ferromagnetic bonds. In the vicinity of this critical point, the size and concentration dependency of the first AND second moment of the domain wall energy are, for both models, described by a COMMON finite size scaling form. Moreover, below this concentration the stiffness exponent turns out to be slightly negative \theta_S = -0.056(6) indicating the absence of any intermediate spin glass phase at non-zero temperature.