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arXiv:1709.02302 · Journal of Physics Conference Series

First-order transition inXYmodel with higher-order interactions

Milan ˇ Zukovič

Published Dec 1, 2017• 1 citation
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Abstract

The effect of inclusion of higher-order interactions in the XY model on critical properties is studied by Monte Carlo simulations. It is found that an increasing number of the higher-order terms in the Hamiltonian modifies the shape of the potential, which beyond a certain value leads to the change of the nature of the transition from continuous to first order. The evidence for the first-order transition is provided in the form of the finite-size scaling and the energy histogram analysis. A rough phase diagram is presented as a function of the number of the higher-order interaction terms.

DOI
10.1088/1742-6596/936/1/012016

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The effect of inclusion of higher-order interactions in the XY model on critical properties is studied by Monte Carlo simulations. It is found that an increasing number of the higher-order terms in the Hamiltonian modifies the shape of the potential, which beyond a certain value leads to the change of the nature of the transition from continuous to first order. The evidence for the first-order transition is provided in the form of the finite-size scaling and the energy histogram analysis. A rough phase diagram is presented as a function of the number of the higher-order interaction terms.
An $x\ensuremath{-}y$ model with nearest-neighbor interaction $V(\ensuremath{\theta})=2J{1\ensuremath{-}{[{cos}^{2}(\frac{\ensuremath{\theta}}{2})]}^{{p}^{2}}}$ is studied by Monte Carlo simulation. The model has a transition from a paramagnetic to an algebraic (massless) phase. An increase of the parameter ppp, which changes the shape of the potential, brings about a change in the nature of the transition from continuous to first order.
Monte Carlo simulation has been performed in a two-dimensional modified XY -model first proposed by Domany [Phys. Rev. Lett. 52, 1535 (1984)] The cluster algorithm of Wolff has been used and multiple histogram reweighting is performed. The first-order scaling behavior of the quantities such as specific heat and free-energy barrier are found to be obeyed accurately. While the lowest-order correlation function was found to decay to zero at long distance just above the transition, the next-higher-order correlation function shows a nonzero plateau.
We have performed Monte Carlo simulation of two planar XY-models using the Wang-Landau algorithm. One of these models is the standard XY-model, the other has a modified potential and exhibits a strongly first order phase transition. The first part of the work is an investigation of the growth of the energy histogram fluctuation in these continuous models. We find that these histograms saturate at values proportional to 1 / √ ( ln f), for both models, irrespective of the width of the energy bin used in the simulation. Next, using the number of Monte Carlo sweeps necessary to attain the saturation value of the histograms, we have obtained the density of states and hence some observables for the two models. PACS: 05.10.Ln, 05.70.Fh, 64.60.Cn 1