In this paper, we apply machine learning methods to study phase transitions in certain
statistical mechanical models on the two-dimensional lattices, whose transitions involve …

Machine learning methods have been recently applied to learning phases of matter and
transitions between them. Of particular interest is the topological phase transition, such as in …

We study the collapse of two-dimensional polymers, via an O (n) model on the square lattice
that allows for dilution, bending rigidity and short-range monomer attractions. This model …

We study a class of loop models, parameterized by a continuously varying loop fugacity n,
on the hydrogen peroxide lattice, which is a three-dimensional cubic lattice of coordination …

We present Tethered Monte Carlo, a simple, general purpose method of computing the
effective potential of the order parameter (Helmholtz free energy). This formalism is based …

We present a Markov-chain Monte Carlo algorithm of worm type that correctly simulates the
O (n) loop model on any (finite and connected) bipartite cubic graph, for any real n> 0, and …

Potts spin systems play a fundamental role in statistical mechanics and quantum field theory
and can be studied within the spin, the Fortuin–Kasteleyn (FK) bond or the q-flow (loop) …

We study the dynamic critical behavior of the Chayes-Machta dynamics for the Fortuin-
Kasteleyn random-cluster model, which generalizes the Swendsen-Wang dynamics for the q …

This thesis is an attempt to provide a new outlook on complex systems, as well as some
physical answers for certain models, taking a computational approach. We have focused on …

We numerically investigate the intriguing effects produced by random percolative disorder in
two-dimensional Josephson junction arrays. By dynamic scaling analysis, we evaluate …