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UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS Guest
2024-11-22 2:37 |
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Conference: Bucharest University Faculty of Physics 2024 Meeting
Section: Polymer Physics
Title:
Exploring Phase Transitions: A Monte Carlo Simulation Approach to the Ising Model
Authors:
Nichita GHEREG, Robert-Antonio IVANESCU, Alexandru-Catalin MACOVEI, Andrada-Maria PUISOR, Andrei TURTICA, Catalin BERLIC
Affiliation:
University of Bucharest, Faculty of Physics, 405 Atomistilor Street, 077125, Magurele, Romania
E-mail
cataliniulian.berlic@g.unibuc.ro
Keywords:
Monte Carlo simulation, Ising model, square lattice, phase transition, magnetization, susceptibility
Abstract:
The study presents an investigation of the Ising model using Monte Carlo simulations to reveal the peculiarities of the phase transition behaviors in both one-dimensional (1D) and two-dimensional (2D) systems. Initially, the Ising model parameters, including interaction strength and magnetic field effects, are outlined, setting the groundwork for simulation scenarios. The Monte Carlo method, particularly the Metropolis algorithm, is employed to simulate the spin interactions and to calculate properties such as energy, magnetization, susceptibility, and heat capacity. In the 1D case, our simulations confirm the absence of a phase transition at finite temperatures, aligning with theoretical predictions. Conversely, the 2D model, simulated on a square lattice, clearly exhibits a phase transition, characterized by a spontaneous magnetization as temperature decreases below the critical value. The critical temperature is estimated and compared with the known exact solution of the 2D Ising model. This work not only reinforces the utility of Monte Carlo simulations in studying statistical physics models but also provides insights into the critical behaviors of low-dimensional systems, potentially guiding future experimental and theoretical research in critical phenomena.
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