Monte Carlo studies of the Ising square lattice with competing interactions

Abstract

We use improved Monte-Carlo algorithms to study the antiferromagnetic 2D-Ising model with competing interactions J1 on nearest neighbour and J2 on next-nearest neighbour bonds. The finite-temperature phase diagram is divided by a critical point at J2 = J1/2 where the groundstate is highly degenerate. To analyse the phase boundaries we look at the specific heat and the energy distribution for various ratios of J2/J1. We find a first order transition for small J2 > J1/2 and the transition temperature suppressed to TC = 0 at the critical point. Neel orderCollinear order NN NNN bonds

Novel mechanism for order patterning in alloys driven by irradiation

“…For R = 0.45, we determine the order-disorder transition temperature for the 2×2 to 1×1 transition to be ≈ 373 K, i.e., 0.643 J 1 /k B , using the fourth-order cumulant method [30]. This value is consistent with previous reports [27,29,31], and it is significantly lower than the value for R = 0, 2/ln(1+√2) J 1 /k B ≈ 2.27 J 1 /k B [32], owing to the frustrations introduced by the second nearest neighbor interaction. [25].…”

“…At finite temperature, the exact nature of the equilibrium boundary between the 2×2 and 2×1 states is complex, with a non-universal behavior [26][27][28]. The work by Kalz et al [29] suggests that this transition is a first order transition, with the critical temperatures of the 2×1 and 2×2 structures going to zero at the boundary.…”

Bicritical Central Point of Ising Model Phase Diagram

“…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.…”