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arXiv:0809.2503 · Journal of Physics Conference Series

Monte Carlo studies of the Ising square lattice with competing interactions

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

Published Jan 1, 2009• 22 citations
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Abstract

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.

DOI
10.1088/1742-6596/145/1/012051

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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.
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The phase transitions in two-dimensional antiferromagnetic Ising model are studied on a square lattice by taking the interactions of next-nearest neighbors into account. The model is investigated on basis of the replica Monte Carlo algorithm and the histogrammic analysis of data. The diagram of the critical temperature dependence on an interaction value of next-nearest neighbors is plotted. The studied model reveals the phase transition of second order and the frustration points depending on relative interaction values and magnetic field. A effect, heat capacity splitting near the frustration points, is found.
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Monte Carlo simulations are used to study the location and nature of phase boundaries for Ising square lattices with antiferromagnetic coupling JNN{J}_{\mathrm{NN}}JNN​ between nearest neighbors and additional interactions JNNN{J}_{\mathrm{NNN}}JNNN​ between next-nearest neighbors and J3NN{J}_{3\mathrm{N}\mathrm{N}}J3NN​ between third-nearest neighbors. Results in zero magnetic field are obtained for a wide range of R=JNNN/JNN{J}_{\mathrm{NNN}/{J}_{\mathrm{NN}}}JNNN/JNN​​ and R'=J3NN/JNN{J}_{3\mathrm{N}\mathrm{N}/{J}_{\mathrm{NN}}}J3NN/JNN​​. In addition to the c(2\ifmmode\times\else\texttimes\fi{}2) and (2\ifmmode\times\else\texttimes\fi{}1) phases, which also occur for R'=0, we find new (4\ifmmode\times\else\texttimes\fi{}4) and (4\ifmmode\times\else\texttimes\fi{}2) ordered states, for R'\ensuremath{\ne}0, which are separated from the disordered state by lines of first-order transitions. The nonuniversal critical behavior of the (2\ifmmode\times\else\texttimes\fi{}1) phase is studied using the block-distribution method and finite-size scaling. The possible existence of incommensurate phases is also explored.