Phase transition induced by an external field in a three-dimensional isotropic Heisenberg antiferromagnet

Abstract

In this paper, we report mean-field and effective-field renormalization group calculations on the isotropic Heisenberg antiferromagnetic model under a longitudinal magnetic field. As is already known, these methods, denoted by MFRG and EFRG, are based on the comparison of two clusters of different sizes, each of them trying to mimic certain Bravais lattice. Our attention has been on the obtention of the critical frontier in the plane of temperature versus magnetic field, for the simple cubic and the body-centered cubic lattices. We used clusters with N = 1, 2, 4 spins so as to implement MFRG-12, EFRG-12 and EFRG-24 numerical equations. Consequently, the resulting frontier lines show that EFRG approach overcomes the MFRG problems when clusters of larger sizes are considered.

The XYZ model in the mean-field approximation in terms of Pauli spin matrices

“…For comparisons with some other works, we were able to compare only the XXX model phase diagram with the works of Refs. [4,5,18,24]. The similarities, especially the existence of a reentrant behaviour, agree with them.…”

“…In addition, a few examples are the rigorous mathematical framework nonperturbative renormalization group (RG) transformations in the finite-temperature regime [2] and the geometric quantum discord for three spin-1/2 particles in the external magnetic field [3]. The critical frontier of the isotropic AFM Heisenberg model in a magnetic field along the z axis was considered by mean field (MF) and effective field theory (EFT) RG calculations [4]. By using the differential operator technique and the EFT scheme, the critical behaviour of amorphous classical Heisenberg ferromagnet in a random field was considered [5].…”

Antiferromagnetic Dispersion Relations and Nature of Magnon Pressure

“…The impact of external magnetic fields on antiferromagnetic systems -both in two and three spatial dimensions -has been studied by various authors employing different techniques: (modified) spin-wave theory [1][2][3][4][5][6][7][8][9][10][11], Green's functions [12][13][14][15][16], series expansions [17][18][19][20], Monte Carlo simulations [21][22][23], exact diagonalization [24,25], and yet other methods [26][27][28][29][30][31][32][33][34][35][36][37].…”