Related papers: Phase transitions in 3D loop models and the $CP^{n…
The presence of nearby conformal field theories (CFTs) hidden in the complex plane of the tuning parameter was recently proposed as an elegant explanation for the ubiquity of "weakly first-order" transitions in condensed matter and…
We study the phase structure of N=1 supersymmetric Yang-Mills theory on R^3XS^1, with massive gauginos, periodic around the S^1, with Sp(2N) (N>=2), Spin(N) (N>=5), G_2, F_4, E_6, E_7, E_8 gauge groups. As the gaugino mass m is increased,…
This thesis investigates critical phenomena and equilibrium states in various stochastic models through three interconnected studies. In the first chapter, we analyze the Activated Random Walk model on a one-dimensional ring in the…
We investigate the phase diagram and critical behavior of a three-dimensional lattice CP(N-1) model in the large-N limit. Numerical evidence of first-order transitions is always observed for sufficiently large values of N, i.e. N>2 up to…
We consider the phase transition in a model which consists of a Ginzburg-Landau free energy for superconductors including a Chern-Simons term. The mean field theory of Halperin, Lubensky and Ma [Phys. Rev. Lett. 32, 292 (1974)] is applied…
The dynamical triangulation model of three-dimensional quantum gravity is shown to have a line of transitions in an expanded phase diagram which includes a coupling mu to the order of the vertices. Monte Carlo renormalization group and…
The model of lattice fermions in 2+1 dimensional space is formulated, the critical states of which are lying in the basis of such physical problems, as 3D Ising Model(3DIM) and the edge excitations in the Hall effect. The action for this…
The values of renormalized Polyakov loops in the three lowest representations of SU(3) were measured numerically on the lattice. We find that in magnitude, condensates respect the large-N property of factorization. In several ways, the…
Large families of integrable 2d sigma-models have been constructed at the classical level, partly motivated by the utility of integrability on the string worldsheet. It is natural to ask whether these theories are renormalisable at the…
The critical dynamics of superconductors in the charged regime is reconsidered within field-theory. For the dynamics the Ginzburg-Landau model with complex order parameter coupled to the gauge field suggested earlier [Lannert et al. Phys.…
By using the results of a high-statistics (O(10^7) measurements) Monte Carlo simulation we test several predictions of perturbation theory on the O(n) non-linear sigma-model in 2 dimensions. We study the O(3) and O(8) models on large enough…
Nienhuis' truncated O(n) model gives rise to a model of self-avoiding loops on the hexagonal lattice, each loop having a fugacity of n. We study such loops subjected to a particular kind of staggered field w, which for n -> infinity has the…
We investigate the one-dimensional finite-size XY model with opposing surface fields in the X direction. Exact solutions are obtained for the two-site and three-site models, while numerical methods are employed for models with more than…
We compute the phase diagram in the N\to\infty limit for lattice RP^{N-1}, CP^{N-1} and QP^{N-1} sigma-models with the quartic action, and more generally for mixed isovector/isotensor models. We show that the N=\infty limit exhibits phase…
We investigate the presence of topological structures and multiple phase transitions in the O(3)-sigma model with the gauge field governed by Maxwell's term and subject to a so-called Gausson's self-dual potential. To carry out this study,…
The nonlinear $\sigma$-model for disordered interacting electrons is studied in spatial dimensions $d>4$. The critical behavior at the metal-insulator transition is determined exactly, and found to be that of a standard…
Motivated by recent work that mapped the low-temperature properties of a class of frustrated spin $S=1$ kagome antiferromagnets with competing exchange and single-ion anisotropies to the fully-packed limit (with each vertex touched by…
The mixed state of superconducting (SC) and normal (N) phases in one dimensional systems are characterized by several phase slips and localization of the order parameter of the SC phase. The phenomenon is explained on the basis of a complex…
We numerically investigate nucleation processes in the transient dynamics of the two-dimensional complex Ginzburg-Landau equation towards its "frozen" state with quasi-stationary spiral structures. We study the transition kinetics from…
This talk is based on a recent paper$^{1}$ of ours. In an attempt to understand three-dimensional conformal field theories, we study in detail one such example --the large $N$ limit of the $O(N)$ non-linear sigma model at its non-trivial…