The Merged Potts-Clock Model: Algebraic and Conventional Multistructured Multicritical Orderings in Two and Three Dimensions

TL;DR

This paper investigates a complex spin system combining Potts and clock interactions in two and three dimensions, revealing a rich phase diagram with multiple ordered phases and multicritical points through advanced renormalization-group analysis.

Contribution

It introduces a novel merged Potts-clock model and provides a detailed phase diagram with multiple multicritical points using improved Migdal-Kadanoff approximation.

Findings

Five distinct ordered phases identified

Multiple multicritical points characterized

Rich phase diagram topology discovered

Abstract

A spin system is studied, with simultaneous permutation-symmetric Potts and spin-rotation-symmetric clock interactions, in spatial dimensions d=2 and 3. The global phase diagram is calculated from the renormalizaton-group solution with the recently improved (spontaneous first-order detecting) Migdal-Kadanoff approximation or, equivalently, with hierarchical lattices with the inclusion of effective vacancies. Five different ordered phases are found: conventionally ordered ferromagnetic, quadrupolar, antiferromagnetic phases and algebraically ordered antiferromagnetic, antiquadrupolar phases. These five different ordered phases and the disordered phase are mutually bounded by first- and second-order phase transitions, themselves delimited by multicritical points: inverted bicritical, zero-temperature bicritical, tricritical, second-order bifurcation, and zero-temperature highly degenerate multicritical points. One rich phase diagram topology exhibits all of these phenomena.