Building a 2D Model Using the Ising Model Concept with Monte Carlo Implementation

This course project implements a two-dimensional Ising model using importance sampling and Monte Carlo methods to simulate ferromagnetic-paramagnetic phase transitions. The code calculates average energy (Ev), heat capacity (Cv), magnetization (M), and magnetic susceptibility (X) for paramagnetic materials, generating Ev-T, Cv-T, M-T, and X-T plots. Key implementations include Metropolis algorithm for spin updates and thermodynamic property computations through statistical averaging.

The Cross-Entropy (CE) Method: Algorithm Overview and Implementation Approaches

The Cross-Entropy (CE) method, pioneered by Reuven Rubinstein, serves as a versatile Monte Carlo technique for combinatorial and continuous multi-extremal optimization, along with importance sampling applications. Originally emerging from rare event simulation domains requiring precise estimation of minuscule probabilities, this method operates through iterative parameter updates using Kullback-Leibler divergence minimization. Key implementation involves sampling from parametric distributions, selecting elite samples based on performance thresholds, and recalculating distribution parameters through maximum likelihood estimation.