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Journal of Physics Conference Series

Phase transitions of 2D triangular antiferromagnetic Ising model in a uniform magnetic field near h=0 and T=0

Wooseop Kwak, Sang-Hyun Kim, Chi‐Ok Hwang

Published Sep 1, 2016• 1 citation
Publisher

Abstract

Using a microcanonical magnetization-energy (ME) diagram, this paper describes all the possible phase transitions of a 2D triangular antiferromagnetic (TAFM) Ising model in a uniform external magnetic field. In particular, we investigate the detailed phase boundary shape of the TAFM near h = 0 and T = 0 using staggered susceptibility.
DOI
10.1088/1742-6596/750/1/012012

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We evaluate the density of states g ( M , E ) as a function of energy E and magnetization M of Ising models on square and triangular lattices, using the exact enumeration method for small systems and the Wang–Landau method for larger systems. From the density of states the average magnetization per spin, m ( T , h ), of the antiferromagnets has been obtained for any values of temperature T and uniform magnetic field h . Also, based on g ( M , E ), the behaviour of m ( T , h ) is understood microcanonically. The microcanonical approach reveals the differences between the unfrustrated model (on the square lattice) and the frustrated one (on the triangular lattice).
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Quantum Ising model on a triangular lattice hosts a finite temperature Berezinskii-Kosterlitz-Thouless (BKT) phase with emergent U(1) symmetry, and it will transit into an up-up-down (UUD) phase with C3{C}_{3}C3​ symmetry breaking upon an infinitesimal external field along the longitudinal direction, but the overall phase diagram spanned by the axes of external field and temperature remains opaque due to the lack of systematic investigations with controlled methodologies. By means of quantum Monte Carlo at finite temperature and ground state density matrix renormalization group simulations, we map out the phase diagram of triangular quantum Ising model. Starting from the upper BKT temperature at zero field, we obtain the phase boundary between the UUD and paramagnetic phases with its 2D q=3q=3q=3 Potts universality at weak field and weakly first order transition at strong field. Originated from the lower BKT temperature at zero field, we analyze the low temperature phase boundary between the clock phase and the UUD phase with Ising symmetry breaking at weak fields and the quantum phase transition between the UUD and fully polarized phases at strong fields. The accurate many-body numerical results are consistent with our field theoretical analysis. The experimental relevance towards the BKT magnet TmMgGaO4{\mathrm{TmMgGaO}}_{4}TmMgGaO4​ and programmable quantum simulators are also discussed.
Monte Carlo simulations of the Ising model on the triangular lattice with the antiferromagnetic nn interaction J and the ferromagnetic nnn interaction J ' are carried out. Several physical quantities (magnetizations, energies, susceptibilities, specific heats of sublattices and of the total system) are calculated. A phase which resembles the partially disordered phase proposed by Mekata is observed in the finite temperature region. But it is shown in this region that the sublattice magnetizations vanish at the thermodynamic limit and the Kosterlitz-Thouless phase transition is predicted by the finite size analysis.