Phase diagram of truncated tetrahedral model

TL;DR

This paper investigates the phase diagram of a discrete spin model based on the truncated tetrahedron, revealing four phases and transitions, using advanced numerical methods to analyze the effects of geometric anisotropy.

Contribution

It introduces a novel analysis of the truncated tetrahedral model's phase diagram using entanglement entropy and corner transfer matrix methods.

Findings

Four distinct phases identified.

Five transition lines between phases.

Weak first-order transition under octahedral anisotropy.

Abstract

Phase diagram of a discrete counterpart of the classical Heisenberg model, the truncated tetrahedral model, is analyzed on the square lattice, when the interaction is ferromagnetic. Each spin is represented by a unit vector that can point to one of the 12 vertices of the truncated tetrahedron, which is a continuous interpolation between the tetrahedron and the octahedron. Phase diagram of the model is determined by means of the statistical analogue of the entanglement entropy, which is numerically calculated by the corner transfer matrix renormalization group method. The obtained phase diagram consists of four different phases, which are separated by five transition lines. In the parameter region, where the octahedral anisotropy is dominant, a weak first-order phase transition is observed.