Phase diagram of the Ising square lattice with competing interactions

Abstract

Abstract. We restudy the phase diagram of the 2D-Ising model with competing interactions J1 on nearest neighbour and J2 on next-nearest neighbour bonds via Monte-Carlo simulations. We present the finite temperature phase diagram and introduce computational methods which allow us to calculate transition temperatures close to the critical point at J2 = J1/2. Further on we investigate the character of the different phase boundaries and find that the transition is weakly first order for moderate J2 > J1/2.

Bicritical Central Point of Ising Model Phase Diagram

“…The phase diagram of Figure 3 shows that obtained critical temperatures agree with the results of studies within Monte Carlo technique [12][13][14][15]23]. Once again finite size scaling analysis confirms an Ising-like behavior with universal critical exponents of the system with R < 0.5 and that order/disorder phase transition for R > 0.5 is nonuniversal (ν = 0.70 and γ = 1.726 ± 0.08 for R = 0.75 for example, the value has to be compared with the one in [12,13]).…”

“…To overcome the status quo and reach a stable low temperature pure phase, it was suggested to improve the jump algorithm by considering parallel tempering method [20]. Here the finite size scaling analysis on the obtained effective critical temperatures concludes an absence of phase transition in the thermodynamic limit [14,15]. In the present, we argue that no pure phase holds rather there are clusters with different ordered structures and sizes that interpenetrate each other well.…”

“…The J FN − J SN Ising model offers a valuable framework for dealing with the phenomena involved as has been confirmed by recent discovery of high-T c superconductivity in pnictides [10,11] (the model helps in dealing with the magnetism of the square Fe sublattice). However, when the interactions between first and second neighboring particles are repulsive in a square lattice the approximations adopted to solve the Ising model give rise to a controversial phase diagram [12][13][14][15][16][17][18]. In fact nowadays everyone agrees that the transition line from the disordered to the ordered p(2 × 2) phase is continuous when the ratio between the second "J SN " and the first "J FN " neighboring interactions R = J SN /J FN < 0.5.…”

“…In fact nowadays everyone agrees that the transition line from the disordered to the ordered p(2 × 2) phase is continuous when the ratio between the second "J SN " and the first "J FN " neighboring interactions R = J SN /J FN < 0.5. The situation R > 0.5 where the degenerate p(2 × 1)/ p(1 × 2) ordered phase holds is still under debate, particularly the extent of interaction rate for which the transition is first order [1,2,[14][15][16][17]19]. In both cases, the characterization of phase transition is done by means of order parameters that quantify the breakdown of lattice occupation symmetry.…”

Фрустрации И Упорядочение В Магнитных Системах Различной Размерности

“…2 представлена фазовая диаграмма для наи-более изученного случая -модели Изинга на квадрат-ной решетке с конкурирующими антиферромагнитными взаимодействиями между ближайшими J < 0 и вторы-ми соседями J ′ < 0 (см., например, [7]). Из расчетов следует, что существует единственная точка фрустраций r = 0.5 (r = J ′ /J), причем нультемпературная энтропия S T →0 равна нулю во всем диапазоне r, в том числе и во фрустрационной точке, а температура фазового перехода во фрустрационной точке равна нулю.…”