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We study a finite-temperature phase transition in the two-dimensional classical Heisenberg model on a triangular lattice with a ferromagnetic nearest-neighbor interaction $J_1$ and an antiferromagnetic third-nearest-neighbor interaction…

Using a Monte Carlo method, we study the finite-temperature phase transition in the two-dimensional classical Heisenberg model on a triangular lattice with or without easy-plane anisotropy. The model takes account of competing interactions:…

We study phase transition behavior of the Heisenberg model on a distorted triangular lattice with competing interactions. The ground-state phase diagram indicates that underlying symmetry can be changed by tuning parameters. We focus on two…

A large part of the interest in magnets with frustrated antiferromagnetic interactions comes from the many new phases found in applied magnetic field. In this Article, we explore some of the new phases which arise in a model with frustrated…

In this work, we investigate the phase transitions and critical behaviors of the frustrated J1-J2-J3 Ising model on the square lattice using Monte Carlo simulations, and particular attention goes to the effect of the second next nearest…

We study a stacked triangular lattice Ising model with both intra- and inter-plane antiferromagnetic interactions in a field, by Monte Carlo simulation. We find only one phase transition from a paramagnetic to a partially disordered phase,…

We study the spin S=1 antiferromagnetic Heisenberg model on the square lattice with, in addition to the nearest-neighbor interaction, a three-site interaction of the form (S_i S_j)*(S_j S_k) + h.c.. This interaction appears naturally in a…

We examine the phase diagram of the spin-$1$ $J_1-J_2-J_3$ ferromagnetic Heisenberg model with an easy-plane crystal field on the cubic lattice, in which $J_1$ is the ferromagnetic exchange interaction between nearest neighbors, $J_2$ is…

We discover an example where the dissociation of the Z2 vortices occurs at the second-order phase transition point. We investigate the nature of phase transition in a classical Heisenberg model on a distorted triangular lattice with…

The phase diagram of the classical anisotropic (XXZ) Heisenberg model on the 2-dimensional triangular lattice is investigated using Monte Carlo methods. In the easy-axis limit, two finite temperature vortex unbinding transitions have been…

The model of localized fermions on the triangular lattice is analyzed in means of the Monte Carlo simulations in the grand canonical ensemble. The Hamiltonian of the system has a form of the extended Hubbard model (at the atomic limit) with…

We examine the $S=1/2$ Heisenberg magnet on four three-dimensional lattices - simple-cubic, diamond, pyrochlore, and hyperkagome ones - for ferromagnetic and antiferromagnetic signs of the exchange interaction in order to illustrate the…

Here we consider the Ising-Heisenberg model in the expanded Kagom\'e lattice, also known as triangle-dodecagon (3-12) or star lattice. This model can still be understood as a decorated honeycomb lattice. Assuming that the Heisenberg spins…

Many frustrated spin models on three-dimensional (3D) lattices are currently being investigated, both experimentally and theoretically, and develop new types of long-range orders in their respective phase diagrams. They present…

We investigate the finite-temperature phase diagram of the classical $J_1$-$J_2$ XY model on a square lattice using a tensor network approach designed for frustrated spin systems. This model, characterized by competing nearest-neighbor and…

We study the phase diagram of the frustrated Heisenberg model on the triangular lattice with nearest and next-nearest neighbor spin exchange coupling, on 3-leg ladders. Using the density-matrix renormalization-group method, we obtain the…

An extensive Monte Carlo study of the classical Heisenberg model on a simple cubic lattice with antiferromagnetic exchange interactions $J_n$ between the first, second, and third neighbors is performed in a broad region of $J_2 / J_1$, $J_3…

We investigate the classical antiferromagnetic Heisenberg model on the triangular lattice with up to third-nearest neighbor exchange couplings using the Nematic Bond Theory. This approach allows us to compute the free energy and the neutron…

We present results from our analysis of the finite-temperature properties of the spin 1/2 $J_{1}$-$J_{2}$ Heisenberg model on a square lattice. The analysis is based on the exact diagonalization of small clusters with 16 and 20 sites…

The classical Heisenberg antiferromagnet on a triangular lattice with the single-ion anisotropy of the easy-axis type is theoretically investigated. The mean-field phase diagram in an external magnetic field is constructed. Three…