Related papers: Renormalisation-induced phase transitions for unim…
We derive the full phase diagram for a large family of two-parameter exponential random graph models, each containing a first order transition curve ending in a critical point.
Fibonacci unimodal maps can have a wild Cantor attractor, and hence be Lebesgue dissipative, depending on the order of the critical point. We present a one-parameter family $f_\lambda$ of countably piecewise linear unimodal Fibonacci maps…
Manifestly invariant renormalization scheme for supersymmetric gauge theories is proposed. This scheme is applied to supersymmetric quantum electrodynamics.
We explore the possibilities of using the fermionic functional renormalization group to compute the phase diagram of systems with competing instabilities. In order to overcome the ubiquituous divergences encountered in RG flows, we propose…
The minimal set of thermodynamic control parameters consists of a statistical (thermal) and a mechanical one. These suffice to introduce all the pertinent thermodynamic variables; thermodynamic processes can then be defined as paths on this…
We compare real and complex dynamics for automorphisms of rational surfaces that are obtained by lifting \chg{some} quadratic birational maps of the plane. In particular, we show how to exploit the existence of an invariant cubic curve to…
Two known distinct examples of one-dimensional systems which are known to exhibit a phase transition are critically examined: (A) a lattice model with harmonic nearest-neighbor elastic interactions and an on-site Morse potential, and (B)…
Any $C^d$ conservative map $f$ of the $d$-dimensional unit ball $\mathbb B^d$ can be realized by renormalized iteration of a $C^d$ perturbation of identity: there exists a conservative diffeomorphism of $\mathbb B^d$, arbitrarily close to…
We obtain estimates relating the phase space and the parameter space of analytic families of unimodal maps. Using those estimates, we show that typical analytic unimodal maps admit a quasiquadratic renormalization. This reduces the study of…
We study the critical behavior of the random q-state Potts model in the large-q limit on the diamond hierarchical lattice with an effective dimensionality $d_{\rm eff} > 2$. By varying the temperature and the strength of the frustration the…
Concerning renormalisation group theory applied to phase transitions, we examine the value of positive numerical and analytical evidence, the divergent short-wavelength behaviour of classical free fields and the absence of UV-divergences in…
Discrete amorphous materials are best described in terms of arbitrary networks which can be embedded in three dimensional space. Investigating the thermodynamic equilibrium as well as non-equilibrium behavior of such materials around second…
We consider parabolic flows on 3-dimensional manifolds which are renormalized by circle extensions of Anosov diffeormorphisms. This class of flows includes nilflows on the Heisenberg nilmanifold which are renormalized by partially…
The topological theory of phase transitions was proposed on the basis of different arguments, the most important of which are: a direct evidence of the relation between topology and phase transitions for some exactly solvable models; an…
A shift-periodic map is a one-dimensional map from the real line to itself which is periodic up to a linear translation and allowed to have singularities. It is shown that iterative sequences $x_{n+1}=F(x_n)$ generated by such maps display…
Uniformity of the probability measure of phase space is considered in the framework of classical equilibrium thermodynamics. For the canonical and the grand canonical ensembles, relations are given between the phase space uniformities and…
The investigation of the Hamiltonian dynamical counterpart of phase transitions, combined with the Riemannian geometrization of Hamiltonian dynamics, has led to a preliminary formulation of a differential-topological theory of phase…
We identify a new universality class of phase transitions that emerges in non-normal systems, extending the classical framework beyond eigenvalue instabilities. Unlike traditional critical phenomena, where transitions occur when eigenvalues…
Consider deterministic random walks F: I x Z -> I x Z, defined by F(x,n)=(f(x), K(x)+n), where f is an expanding Markov map on the interval I and K: I->Z. We study the universality (stability) of ergodic (for instance, recurrence and…
Many thermodynamic instabilities in one dimension (e.g. DNA thermal denaturation, wetting of interfaces) can be described in terms of simple models involving harmonic coupling between nearest neighbors and an asymmetric on-site potential…