Metropolis-Hasting algorithm for simulating Clock Model and estimation of critical exponents.
The Monte Carlo method has long been recognised as a powerful technique for performing certain calculations, generally those too complicated for a more classical approach. Since the use of high-speed computers became widespread in the 1950s, a great deal of theoretical investigation has been undertaken and practical experience has been gained in the Monte Carlo approach. Monte Carlo methods are being essential as computational tools in physics, enabling the simulation of a wide range of systems, from simple spin models to complex theories of fundamental forces and spacetime. This report provides an overview of the Monte Carlo approach, beginning with basic algorithms like Metropolis-Hastings applied to models such as the Zn lattice and spin glasses, which is widely used to study phase transitions and critical behaviour in statistical mechanics. As simulations extend to more complex systems, including lattice field theories, advanced techniques like cluster algorithms, replica exchange, and Hybrid Monte Carlo become necessary to efficiently explore the vast and intricate configuration spaces of these models.
We highlight how these algorithms have expanded the applicability of Monte Carlo methods, allowing physicists to investigate fundamental interactions, particle behaviour, and even aspects of quantum gravity. By examining this progression from simpler models to more abstract applications, the report illustrates the flexibility and growing importance of Monte Carlo simulations in modern physics.
Below gif is the simulation of Ising system (Z-2 model) with varying temperature (T/T0). Alongside, simulating the change in instantenous energy and magnetization of the system.
Below is the link containing all the refered sources and previous versions of codes and report:
PHY-F313 Computational Physics Assignment