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arXiv:0805.0983 · The European Physical Journal B

Phase diagram of the Ising square lattice with competing interactions

Ansgar Kalz, A. Honecker, Sebastian Fuchs, Thomas Pruschke

Published Oct 1, 2008• 68 citations
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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 criticalpoint at J2 = J1/2. Further on we investigate the character of the different phase boundariesand find that the transition is weakly first order formoderate J2 > J1/2.

DOI
10.1140/epjb/e2008-00359-6

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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 criticalpoint at J2 = J1/2. Further on we investigate the character of the different phase boundariesand find that the transition is weakly first order formoderate J2 > J1/2.
We use improved Monte-Carlo algorithms to study the antiferromagnetic 2D-Ising model with competing interactions J 1 on nearest neighbour and J 2 on next-nearest neighbour bonds. The finite-temperature phase diagram is divided by a critical point at J 2 = J 1 /2 where the groundstate is highly degenerate. To analyse the phase boundaries we look at the speciflc heat and the energy distribution for various ratios of J 2 / 1 . We find a first order transition for small J 2 > J 1 /2 and the transition temperature suppressed to T C = 0 at the critical point.
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. 1.
We analyze the phase transition of the frustrated J1{J}_{1}J1​-J2{J}_{2}J2​ Ising model with antiferromagnetic nearest- and strong next-nearest-neighbor interactions on the square lattice. Using extensive Monte Carlo simulations we show that the nature of the phase transition for $1/2<{J}_{2}/{J}_{1}\ensuremath{\lesssim}1$ is not of the weakly universal type---as commonly believed---but we conclude from the clearly doubly peaked structure of the energy histograms that the transition is of weak first order. Motivated by these results, we analyze the phase transitions via field-theoretic methods; i.e., we calculate the central charge of the underlying field theory via transfer-matrix techniques and present, furthermore, a field-theoretic discussion on the phase-transition behavior of the model. Starting from the conformally invariant fixed point of two decoupled critical Ising models (J1=0{J}_{1}=0J1​=0), we calculate the effect of the nearest-neighbor coupling term perturbatively using operator product expansions. As an effective action we obtain the Ashkin-Teller model.
The phase diagram of the Ising square lattice with first- and second-nearest-neighbor antiferromagnetic interactions (J1{\mathit{J}}_{1}J1​ and J2{\mathit{J}}_{2}J2​) is calculated within the framework of the cluster-variation method. The Hamiltonian is solved within the nine-point-cluster approximation. In contrast to previous studies we find that the phase transition from the superantiferromagnetic to the paramagnetic state is of first order in the range 0.5R=J1{\mathit{J}}_{1}J1​/${\mathit{J}}_{2}$1.144. The non-Ising critical behavior observed in that range of interactions might be due to that phenomenon.
Phase transitions of the spin-one Ising model with nearest-neighbour and next-nearest-neighbour interactions are investigated for a square lattice using a molecular-field theory and a Monte Carlo method. Special attention is paid to the effects of the biquadratic next-nearest-neighbour interaction on the phase transitions of the model. Phase diagrams characterizing types of phase transition are obtained for several values of the coupling constants. The existence of the multi-critical points and the successive phase transitions are also discussed in connection with these phase diagrams.