The Chiral Potts Spin Glass in d=2 and 3 Dimensions

TL;DR

This study uses renormalization-group theory to analyze the phase diagrams of a 3D chiral Potts spin-glass system, revealing complex phase structures, chaos behavior, and differences between 2D and 3D cases.

Contribution

It provides the first detailed phase diagram and chaos analysis for the 3D chiral Potts spin-glass, highlighting microreentrances and unique Lyapunov exponents.

Findings

In 3D, multiple ordered phases including chiral spin-glass are identified.

Chaotic interaction behavior is characterized with reversed Lyapunov exponents.

In 2D, no spin-glass phase exists, consistent with lower critical dimension.

Abstract

The chiral spin-glass Potts system with q=3 states is studied in d=2 and 3 spatial dimensions by renormalization-group theory and the global phase diagrams are calculated in temperature, chirality concentration p, and chirality-breaking concentration c, with determination of phase chaos and phase-boundary chaos. In d=3, the system has ferromagnetic, left-chiral, right-chiral, chiral spin-glass, and disordered phases. The phase boundaries to the ferromagnetic, left- and right-chiral phases show, differently, an unusual, fibrous patchwork (microreentrances) of all four (ferromagnetic, left-chiral, right-chiral, chiral spin-glass) ordered ordered phases, especially in the multicritical region. The chaotic behavior of the interactions, under scale change, are determined in the chiral spin-glass phase and on the boundary between the chiral spin-glass and disordered phases, showing Lyapunov exponents in magnitudes reversed from the usual ferromagnetic-antiferromagnetic spin-glass systems. At low temperatures, the boundaries of the left- and right-chiral phases become thresholded in p and c. In the d=2, the chiral spin-glass system does not have a spin-glass phase, consistently with the lower-critical dimension of ferromagnetic-antiferromagnetic spin glasses. The left- and right-chirally ordered phases show reentrance in chirality concentration p.