Monte Carlo simulation on 2D XY-model. Vortices and anti-vortices correspond to the singular points (defects) where all colors meet together. At low temperatures we observe that spins rearrange themselves in either blobs (phase separation) or stripes, depending on the strength of the second nearest neighbor repulsion. We use optional third-party analytics cookies to understand how you use GitHub.com so we can build better products. KEYWORDS: classical XY model, Kosterlitz-Thouless transition, Monte Carlo simulation, cluster algorithm, finite-size scaling, parallel computing, multiple GPU calculation The two-dimensional (2D) classical XY model (planar ro-tator model) shows a unique phase transition, the Kosterlitz-Thouless (KT) transition.1,2) It does not have true long-range the Monte Carlo method aims to reproduce the statistical behavior of a system at the thermodynamic equilibrium. An extensive discussion of the fundamental and technical problems that arise in simulations of 1D spin-l/2 models (XY and Heisenberg models) can be found in ref. L.A.S. The temperature dependence of the energy (3D Ising model) The temperature dependence of the magnetization (3D Ising model) XY model This model is an ideal system which consists of spins which can face in any directions. Simulating systems up to the linear system size L = 65536, we investigate the Kosterlitz-Thouless (KT) transition. the Monte Carlo method aims to reproduce the statistical behavior of a system at the thermodynamic equilibrium. Using Monte Carlo simulations, we study the effect of introducing annealed disorder and a second nearest neighbor repulsion between spins on a two-dimensional site-diluted XY model. PHYSICA ELSEVIER Physica A 246 (1997) 633~45 Monte Carlo study of asymmetric 2D XY model Christian Holma, Wolfhard Jankeb,c,*, Tetsuo Matsuid, Kazuhiko Sakakibarae a Max-Planek-lnstitut J~ir Polymerforsehung, Postjach 3148, 55021 Mainz, German), b Institut J~ir Physik, Johannes Gutenberg-Universitiit Mainz, Staudinyer Weg 7, 55099 Mainz, Germany c Institut flit Theoretische … Microcanonical Monte Carlo simulations have been carried out on the 2d classical XY -model. You signed in with another tab or window. Monte Carlo simulations with this type of representa- tion. they're used to log you in. Simulations were carried out on a square lattice having 25, 100 or 900-spins with periodic boundary conditions. Keywords : Monte Carlo simulations, 2d XY-model, fluctuation PACS Nos. It exhibits an infinite order phase transition from a disordered high-temperature phase to a quasi-long range ordered low-temperature phase that consists of a line of fixed points. Simulations on various system sizes confirm an earlier observation that the maximum in the temperature dependence of the specific heat is determined primarily by the temperature dependence of the vortex density (V). The 2D XY model is one of the most interesting cases of a statistical mechanics problem whose properties can be used to demonstrate a wide variety of important ideas which are pervasive throughout other areas of many-body physics. Monte Carlo Renormalization Group Study of the 2D XY Model Ryan Young 3/10/2011 The 2D XY model is a well understood yet sophisticated statistical spin model. To that purpose, an algorithm randomly samples configura- ... of the 2D XY model, and show that transitions in 2D are not universal. ... of the 2D XY model, and show that transitions in 2D are not universal. 1. Similar to the Ising model spins with different orientation φ are painted in different colors Hue(φ/2π). self.equilibrate(self,max_nsweeps=int(1e4),temperature=None,H=None,show = False) allows you to assign a new temperature, just simply do object.equilibrate(temperature = 3). Finally, I address the question of the nature of the melting transition of 2D solids. The 2D XY model has also been studied in great detail using Monte Carlo simulations, for example with the Metropolis algorithm. Learn more. : Monte Carlo study of 2D generalized XY-models 543 Fig. sohw=Ture` will let show the configuration of the system for each 1000 sweeps. We have simulated two-dimensional classical XY-model in a microcanonical ensemble using the Monte Carlo technique. model using both numerical Monte Carlo techniques and various analytical techniques. For more information, see our Privacy Statement. We use optional third-party analytics cookies to understand how you use GitHub.com so we can build better products. You can always update your selection by clicking Cookie Preferences at the bottom of the page. [12]. sohw=Ture` will let show the configuration of the system for each 1000 sweeps. Contribute to Shiling42/XY-MODEL development by creating an account on GitHub. For the d-dimensional XY model we have found Learn more. This program runs same algorithm as 2D Ising model, but extended to 3 dimensions. M´ol et al. We study the two-dimensional classical XY model by the large-scale Monte Carlo simulation of the Swendsen-Wang multi-cluster algorithm using multiple GPUs on the open science supercomputer TSUBAME 2.0. the 2d classical XY-model We suggest an alternative equilibration check and demonstrate that the system energy distribution is a Boltzmannian. Now, let the system evolve to a equilibrium state. download the GitHub extension for Visual Studio. Monte Carlo simulation on 2D XY-model. These can be used to compute thermodynamic quantities like the system energy, specific heat, magnetization, etc., over a range of temperatures and time-scales. Finally, I address the question of the nature of the melting transition of 2D solids. The nearest neighbour interaction potential was taken to beV(θ)=2J[1−cos100(θ/2)]. 02.70 Lq. In this paper we study a recent generalization of the XY-model in two dimensions by using Monte Carlo method. The vortex density, specific heat, energy and critical temperature are obtained. 05.70 Fh Computer simulation has become very powerful and inevitable branch in theoretical physics of late. Vortex density as a function of the exponent q for T =0.90 J and several values of L.Thecurveisgivenby equation (4) and correspond to the fit for L =96withthe values given in Table 1. If you want to keep the temperature defined before, leave it blank. We use essential cookies to perform essential website functions, e.g. Learn more, We use analytics cookies to understand how you use our websites so we can make them better, e.g. : 75 10 Hk. they're used to gather information about the pages you visit and how many clicks you need to accomplish a task. The system energy, mean square magnetization and vortex-density were … Monte-Carlo simulations of spins dynamics in the XY magnetic model. For T = 0.03 "hot" (random) spins are frozen in correlated clusters. Important physics behind super

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