Second order phase transition in the six-dimensional Ising spin glass on a field

Miguel Aguilar-Janita, Victor Martin-Mayor, Javier Moreno-Gordo, Juan Jesus Ruiz-Lorenzo

Published 2023-06-01Version 1

The very existence of a phase transition for spin glasses in an external magnetic field is controversial, even in high dimensions. We carry out massive simulations of the Ising spin-glass in a field, in six dimensions (which, according to classical, but not generally accepted, field-theoretical studies, is the upper critical dimension). We find a phase transition and compute the critical exponents, that are found to be compatible with their mean-field values. We also find that the replica-symmetric Hamiltonian describes the scaling of the renormalized couplings near the phase transition.