Related papers: Nonuniversality in random criticality
The anisotropic two-layer Ising model is studied by the phenomenological renormalizaiton group method. It is found that the anisotropic two-layer Ising model with symmetric couplings belongs to the same universality class as the two…
To establish a unified framework for studying both discrete and continuous coupling distributions, we introduce the {\it binomial} spin glass, a class of models where the couplings are sums of $m$ identically distributed Bernoulli random…
We propose a new picture of the renormalization group (RG) approach in the presence of disorder, which considers the RG trajectories of each random sample (realization) separately instead of the usual renormalization of the averaged free…
Disordered systems are interesting for many physical reasons. In this article, we study the renormalization group property of quenched disorder systems in the presence of a boundary. We construct examples of scalar field theories in various…
We use scale invariant scattering theory to exactly determine the renormalization group fixed points of a $q$-state Potts model coupled to an $r$-state Potts model in two dimensions. For integer values of $q$ and $r$ the fixed point…
We consider m two-dimensional semi-infinite planes of Ising spins joined together through surface spins and study the critical behaviour near to the junction. The m=0 limit of the model - according to the replica trick - corresponds to the…
The scaling form of the free-energy near a critical point allows for the definition of various thermodynamical amplitudes and the determination of their dependence on the microscopic non-universal scales. Universal quantities can be…
Randomly coupled Ising spins constitute the classical model of collective phenomena in disordered systems, with applications covering ferromagnetism, combinatorial optimization, protein folding, stock market dynamics, and social dynamics.…
The Lee-Yang circle theorem revolutionized our understanding of phase transitions in ferromagnetic systems by showing that the complex zeros of partition functions lie on the unit circle, with criticality arising as these zeros approach the…
A system defined by two coupled Ising models, with a bimodal random field acting in one of them, is investigated. The interactions among variables of each Ising system are infinite-ranged, a limit where mean field becomes exact. This model…
We employ the nonperturbative functional Renormalization Group to study models with an O(N_1)+O(N_2) symmetry. Here, different fixed points exist in three dimensions, corresponding to bicritical and tetracritical behavior induced by the…
We employ the machinery of smooth scaling and coarse-graining of observables, developed recently by us in the context of so-called fluctuation operators (inspired by prior work of Verbeure et al) to make a rigorous renormalisation group…
We introduce three non-local observables for the two-dimensional Ising model. At criticality, conformal field theory may be used to obtain theoretical predictions for their behavior. These formulae are explicit enough to show that their…
Using large-scale Monte Carlo simulations that combine parallel tempering with specialized cluster updates, we show that Ising spin glasses with Levy-distributed interactions share the same universality class as Ising spin glasses with…
We present a unifying, consistent, finite-size-scaling picture for percolation theory bringing it into the framework of a general, renormalization-group-based, scaling scheme for systems above their upper critical dimensions $d_c$.…
Critical points and singularities are encountered in the study of critical phenomena in probability and physics. We present recent results concerning the values of such critical points and the nature of the singularities for two prominent…
The contact process and the slightly different susceptible-infected-susceptible model are studied on long-range connected networks in the presence of random transition rates by means of a strong disorder renormalization group method and…
We investigate the effects of quenched randomness on topological quantum phase transitions in strongly interacting two-dimensional systems. We focus first on transitions driven by the condensation of a subset of fractionalized…
We introduce an exact replica method for the study of critical systems with quenched bond randomness in two dimensions. For the $q$-state Potts model we show that a line of renormalization group fixed points interpolates from weak to strong…
We examine the Jarzynski equality for a quenching process across the critical point of second-order phase transitions, where absolute irreversibility and the effect of finite-sampling of the initial equilibrium distribution arise on an…