Critical behavior of the two-dimensional icosahedron model

TL;DR

This study investigates the critical behavior of a two-dimensional icosahedron spin model, revealing a second-order phase transition with unique critical exponents and a central charge not fitting standard conformal field theories.

Contribution

The paper introduces a detailed analysis of the icosahedron model's critical behavior using CTMRG, highlighting novel critical exponents and a non-standard central charge.

Findings

Second-order phase transition identified with specific critical exponents.

Central charge estimated at approximately 1.90, outside minimal conformal field theory series.

Critical behavior characterized by correlation length and magnetization scaling.

Abstract

In the context of a discrete analogue of the classical Heisenberg model, we investigate critical behavior of the icosahedron model, where the interaction energy is defined as the inner product of neighboring vector spins of unit length pointing to vertices of the icosahedron. Effective correlation length and magnetization of the model are calculated by means of the corner-transfer matrix renormalization group (CTMRG) method. Scaling analysis with respect to the cutoff dimension $m$ in CTMRG reveals the second-order phase transition characterized by the exponents $\nu = 1.62\pm0.02$ and $\beta = 0.12\pm0.01$. We also extract the central charge from the classical analogue of the entanglement entropy as $c = 1.90\pm0.02$, which cannot be explained by the minimal series of conformal field theory.