Phase transition of the four-dimensional cross-polytope model

TL;DR

This study investigates the thermodynamic phase transition of the four-dimensional cross-polytope model, confirming a first-order transition and showing that latent heat increases with internal dimension.

Contribution

It provides the first detailed analysis of the four-dimensional cross-polytope model's phase transition using CTMRG, extending understanding of higher-dimensional polytope models.

Findings

Confirmed first-order phase transition in the 4D cross-polytope model

Estimated latent heat of 0.3172, larger than in 3D

Latent heat increases with internal dimension n

Abstract

Thermodynamic properties of the four-dimensional cross-polytope model, the 16-cell model, which is an example of higher dimensional generalizations of the octahedron model, are studied on the square lattice. By means of the corner transfer matrix renormalization group (CTMRG) method, presence of the first-order phase transition is confirmed. The latent heat is estimated to be $L_4^{~} = 0.3172$, which is larger than that of the octahedron model $L_3^{~} = 0.0516$. The result suggests that the latent heat increases with the internal dimension $n$ when the higher-dimensional series of the cross-polytope models is considered.