Related papers: Critical Phenomena in Hyperbolic Space
A system of N classical particles in a 2D periodic cell interacting via long-range attractive potential is studied. For low energy density $U$ a collapsed phase is identified, while in the high energy limit the particles are homogeneously…
Taking the two-dimensional $\phi^4$ theory as an example, we numerically solve the deterministic equations of motion with random initial states. Short-time behavior of the solutions is systematically investigated. Assuming that the…
We study two-dimensional systems with boundary curves described by power laws. Using conformal mappings we obtain the correlations at the bulk critical point. Three different classes of behaviour are found and explained by scaling arguments…
We study renormalization group multicritical fixed points in the $\epsilon$-expansion of scalar field theories characterized by the symmetry of the (hyper)cubic point group $H_N$. After reviewing the algebra of $H_N$-invariant polynomials…
We investigate the effects of geometric fluctuations, associated with aperiodic exchange interactions, on the critical behavior of $q$-state ferromagnetic Potts models on generalized diamond hierarchical lattices. For layered exchange…
Universality and scaling are hallmarks of second-order phase transitions but are generally unexpected in first-order quantum phase transitions (FOQPTs). We present a microscopic theory showing that quantum criticality can emerge around the…
The second-order phase transitions in the Ising model and liquid-gas systems share a universality class and critical exponents, despite the absence of $Z_2$ symmetry in the liquid-gas Hamiltonian. This discrepancy highlights a central…
We study the phase diagram and critical behavior of the two-dimensional square-lattice fully frustrated XY model (FFXY) and of two related models, a lattice discretization of the Landau-Ginzburg-Wilson Hamiltonian for the critical modes of…
Critical behaviour of a fluid, subjected to strongly anisotropic turbulent mixing, is studied by means of the field theoretic renormalization group. As a simplified model, relaxational stochastic dynamics of a non-conserved scalar order…
The interest in the topological properties of materials brings into question the problem of topological phase transitions. As a control parameter is varied, one may drive a system through phases with different topological properties. What…
The mean-field optical phase transition in multimode equal-coupling photonic networks is studied by temporal evolution of the nonlinear equations of motion of the coupled modes. Analogies to statistical mechanics models of interacting…
We present a simple argument which determines the critical value of the anomaly coefficient in four dimensional conformal factor quantum gravity, at which a phase transition between a smooth and elongated phase should occur. The argument is…
The stickiness effect suffered by chaotic orbits diffusing in the phase space of a dynamical system is studied in this paper. Previous works have shown that the hyperbolic structures in the phase space play an essential role in causing the…
We model two-dimensional systems of granular aggregates confined between two planes and demonstrate that at a critical grain volume fraction an abrupt rigidity transition occurs. This transition is observed both in static and shear tests.…
In the 1960's, four famous scaling relations were developed which relate the six standard critical exponents describing continuous phase transitions in the thermodynamic limit of statistical physics models. They are well understood at a…
In this thesis, we explore the critical phenomena in the presence of extended objects, which we call defects, aiming for a better understanding of the properties of non-local objects ubiquitous in our world and a more practical and…
We consider a particle moving in $d\geq 2$ dimensions, its velocity being a reversible diffusion process, with identity diffusion coefficient, of which the invariant measure behaves, roughly, like $(1+|v|)^{-\beta}$ as $|v|\to \infty$, for…
Above the upper critical dimension, the breakdown of hyperscaling is associated with dangerous irrelevant variables in the renormalization group formalism at least for systems with periodic boundary conditions. While these have been…
XY frustrated magnets exhibit an unsual critical behavior: they display scaling laws accompanied by nonuniversal critical exponents and a negative anomalous dimension. This suggests that they undergo weak first order phase transitions. We…
The critical behaviour of three-dimensional disordered systems is investigated by analysing the spectral fluctuations of the energy spectrum. Our results suggest that the initial symmetries (orthogonal, unitary and symplectic) are broken by…