Low-Temperature Phase Boundary of dilute Lattice Spin Glasses

TL;DR

This paper investigates the critical behavior of dilute lattice spin glasses near the percolation threshold, providing extensive simulations across multiple dimensions to test theoretical predictions about phase transitions and scaling exponents.

Contribution

The study offers new high-precision estimates of the crossover exponent  for Edwards-Anderson spin glasses at p_c, extending simulations to very large system sizes and analyzing the transition temperature scaling.

Findings

Estimated =1.127(5) in three dimensions.

Provided scaling relations for transition temperature T_g near p_c.

Challenged existing mean-field theories in higher dimensions.

Abstract

The thermal-to-percolative crossover exponent \phi, well-known for ferromagnetic systems, is studied extensively for Edwards-Anderson spin glasses. The scaling of defect energies are determined at the bond percolation threshold p_c, using an improved algorithm. Simulations extend to system sizes above N=10^8 in dimensions d=2,...,7. The results can be related to the behavior of the transition temperature T_g (p-p_c)^\phi between the paramagnetic and the glassy regime for p-> p_c. In three dimensions, where our simulations predict \phi=1.127(5), this scaling form for T_g provides a rare experimental test of predictions arising from the equilibrium theory of low-temperature spin glasses. For dimension near and above the upper critical dimension, the results provide a new challenge to reconcile mean-field theory with finite-dimensional properties.