Spinodal and Equilibrium Global Phase Diagram of the d=3 Merged Potts-Cubic-Clock Model: First-Order Equilibrium and Second-Order Spinodal Boundaries with Hidden Topologies from Renormalization-Group Theory

TL;DR

This study uses renormalization-group theory to analyze a merged Potts-cubic-clock model in three dimensions, revealing complex phase boundaries, multiple phases, and the effects of vacancies on phase transitions and spinodal behavior.

Contribution

It introduces a comprehensive phase diagram for the merged model, including first- and second-order boundaries, and explores the impact of vacancies on phase transition nature and topology.

Findings

Identification of 5 ordered phases and a disordered phase with various phase boundaries.

Discovery of 17 phase diagram cross-sections in the spinodal phase diagram.

Reentrant behavior of ferrimagnetic and antiferrimagnetic phases in the spinodal diagram.

Abstract

A model that merges the Potts, cubic, and clock models is studied in spatial dimension d=3 by renormalization-group theory. Effective vacancies are included in the renormalization-group initial conditions. In the global phase diagram, 5 different ordered phases, namely ferromagnetic, antiferromagnetic, ferrimagnetic, antiferrimagnetic, axial, and a disordered phase are found, separated by first- and second-order phase boundaries. 8 different phase diagram cross-sections occur. When the effective vacancies are suppressed, the global spinodal phase diagram is found: All disordering phase transitions become second order, the disordered phase recedes, and 17 different phase diagram cross-sections occur, spinodality thus much enriching ordering behavior. In the spinodal phase diagram, the ferrimagnetic and antiferrimagnetic phases have reentrance. The employed renormalization group transformation is exact on the d=3 dimensional hierarchical model and Migdal-Kadanoff approximate on the cubic lattice.