No spin-glass transition in the "mobile-bond" model

TL;DR

This study uses large-scale ground-state calculations to investigate the mobile-bond model for 2D spin glasses, finding no evidence of a finite-temperature spin-glass transition contrary to previous claims based on smaller systems.

Contribution

It provides the first large-system ground-state analysis of the mobile-bond model, clarifying its phase behavior and disproving the existence of a finite-temperature transition.

Findings

No finite-temperature spin-glass transition for T_q>=0.95

System behaves like a ferromagnet with frustrated plaquettes at low T_q

Results contradict earlier Monte Carlo simulation claims

Abstract

The recently introduced ``mobile-bond'' model for two-dimensional spin glasses is studied. The model is characterized by an annealing temperature T_q. On the basis of Monte Carlo simulations of small systems it has been claimed that this model exhibits a non-trivial spin-glass transition at finite temperature for small values of T_q. Here the model is studied by means of exact ground-state calculations of large systems up to N=256^2. The scaling of domain-wall energies is investigated as a function of the system size. For small values T_q<0.95 the system behaves like a (gauge-transformed) ferromagnet having a small fraction of frustrated plaquettes. For T_q>=0.95 the system behaves like the standard two-dimensional +-J spin-glass, i.e. it does NOT exhibit a phase transition at T>0.