Stability of Universality Classes under perturbations of Markov Chain Monte Carlo

Markov Chain Monte Carlo (MCMC) methods, supplemented by Finite Size Scaling (FSS) analyses, are standard techniques to investigate universal behaviours arising near critical phenomena. Despite the success of this approach, real simulations are affected by specific systematic errors which are typically not taken into account. These systematic errors are related to the finite numerical precision (truncation errors) of the hardware used and, possibly, stochastic hardware noises. In standard CPUs, and more generally in classical hardware, the truncation error is the main source of error, while in a quantum computing environment stochastic noises have also to be taken into account. The aim of this thesis is to study how these systematic errors affect the behaviour of the simulated Markov chain. In particular, we are interested in investigating whether, and eventually how, these systematic errors influence the determination of universal properties. In order to study this issue we use as testbed the three-dimensional XY model. Results obtained using a standard 64-bit precision IEEE hardware have been compared with the results obtained by artificially reducing the numerical accuracy or by introducing a Gaussian noise in the Markov chain transition probability. Remarkably, we find that universal properties are robust under these perturbations, while non-universal properties, like the value of the critical temperature, are always altered by them.