Domain State of the ANNNI model in Two Dimensions

TL;DR

This study investigates the spin ordering and phase transitions of the 2D ANNNI model near the antiphase, revealing a domain state with diverse spin structures and weak XY symmetry breaking, using Monte Carlo simulations.

Contribution

It provides the first detailed analysis of the domain state and transition temperature in the 2D ANNNI model near the antiphase using a cluster heat bath Monte Carlo method.

Findings

Transition temperature T_{C2}/J = 0.89 ± 0.01

Identification of a domain state with four types of domains

Weak breaking of 2D XY symmetry in the IC phase

Abstract

We have examined the spin ordering of an axial next-nearest-neighbor Ising (ANNNI) model in two dimensions (2D) near above the antiphase ($\langle 2 \rangle$ phase). We considered an $N_R$-replica system and calculated an overlap function $q_m$ between different replicas having used a cluster heat bath (CHB) Monte Carlo method. We determined transition temperature between $\langle 2 \rangle$ phase and a floating incommensurate (IC) phase as $T_{C2}/J = 0.89 \pm 0.01$ with frustration ratio $\kappa (\equiv -J_2/J_1) = 0.6$. We found that the spin state at $T \gtrsim T_{C2}$ may be called as a domain state, because the spin structure is characterized by a sequentially arranged four types of domains with different $\langle 2 \rangle$ structures. In the domain state, the 2D XY symmetry of the spin correlation in the IC phase weakly breaks and the diversity of the spin arrangement increases as $T \rightarrow T_{C2}$. The Binder ratio $g_L$ exhibits a depression at $T \sim T_{C2}$ and the quasi-periodic spin structure, which is realized in the IC phase, becomes diverse at $T \gtrsim T_{C2}$. We discussed that the domain state is stable against the thermal fluctuation which brings a two-stage development of the spin structure at low temperatures.