Reentrant and Forward Phase Diagrams of the Anisotropic Three-Dimensional Ising Spin Glass

TL;DR

This paper provides an exact solution for the phase diagram of a three-dimensional anisotropic Ising spin glass on a hierarchical lattice, revealing five ordered phases and complex boundary behaviors including reentrant and forward transitions.

Contribution

It introduces an exact analysis of the phase diagram for the anisotropic 3D Ising spin glass, highlighting the influence of anisotropy and Nishimori symmetry on phase boundaries.

Findings

Five distinct ordered phases identified.

Spin-glass phase extends more with in-plane randomness.

Reentrant and forward phase boundaries observed.

Abstract

The spatially uniaxially anisotropic d=3 Ising spin glass is solved exactly on a hierarchical lattice. Five different ordered phases, namely ferromagnetic, columnar, layered, antiferromagnetic, and spin-glass phases, are found in the global phase diagram. The spin-glass phase is more extensive when randomness is introduced within the planes than when it is introduced in lines along one direction. Phase diagram cross-sections, with no Nishimori symmetry, with Nishimori symmetry lines, or entirely imbedded into Nishimori symmetry, are studied. The boundary between the ferromagnetic and spin-glass phases can be either reentrant or forward, that is either receding from or penetrating into the spin-glass phase, as temperature is lowered. However, this boundary is always reentrant when the multicritical point terminating it is on the Nishimori symmetry line.