Related papers: On the Simple Approach to Critical Phenomena Descr…
Most of the analytical studies on spin glasses are performed by using mean-field theory and renormalization group analysis. Analytical studies on finite-dimensional spin glasses are very challenging. In this short note, a possible exten-…
Hysteresis is observed at second order phase transitions. Universal scaling formul\ae{} for the areas of hysteresis loops are written down. Critical exponents are defined, and related to other exponents for static and dynamic critical…
Chiral perturbation theory is a very general expansion method which can be applied to any dynamical system which has continuous global symmetries and in which the ground state breaks some of these spontaneously. In these lectures we explain…
In the Landau theory of phase transitions one considers an effective potential $\Phi$ whose symmetry group $G$ and degree $d$ depend on the system under consideration; generally speaking, $\Phi$ is the most general $G$-invariant polynomial…
An explicit expression is derived for the statistical description of small quantum systems, which are relatively-weakly and directly coupled to only small parts of their environments. The derived expression has a canonical form, but is…
We study the time evolution of thermodynamic observables that characterise the dissipative nature of thermal relaxation after an instantaneous temperature quench. Combining tools from stochastic thermodynamics and large-deviation theory, we…
General properties of perturbed conformal field theory interacting with quantized Liouville gravity are considered in the simplest case of spherical topology. We discuss both short distance and large distance asymptotic of the partition…
An exact solution of a Landau model of an order-disorder transition with activated critical dynamics is presented. The model describes a funnel-shaped topography of the order parameter space in which the number of energy lowering…
Shape inference is classically ill-posed, because it involves a map from the (2D) image domain to the (3D) world. Standard approaches regularize this problem by either assuming a prior on lighting and rendering or restricting the domain,…
We consider a multi-scalar field theory with either short-range or long-range free action and with quartic interactions that are invariant under $O(N_1)\times O(N_2) \times O(N_3)$ transformations, of which the scalar fields form a…
Critical transitions, or large changes in the state of a system after a small change in the system's external conditions or parameters, commonly occur in a wide variety of disciplines, from the biological and social sciences to physics.…
We analyse a proposition which considers quantum theory as a mere tool for calculating probabilities for sequences of outcomes of observations made by an Observer, who him/herself remains outside the scope of the theory. Predictions are…
In this study, we present theoretical investigations of phase transitions and critical phenomena in materials through the lens of second-order Ginzburg-Landau theory, in conjunction with considerations of symmetry groups and thermal…
Rovelli's relational interpretation of quantum mechanics tells us that the description of a system in the formalism of quantum mechanics is not an absolute, but it is relative to the observer itself. The interpretation goes further and…
The perturbative dynamics of quantum field theories is described by a recursive expansion similar to the well known loop expansion. The equivalent formulation based on low-energy dynamics via an expansion in derivatives is well known in the…
Continuum models with critical end points are considered whose Hamiltonian ${\mathcal{H}}[\phi,\psi]$ depends on two densities $\phi$ and $\psi$. Field-theoretic methods are used to show the equivalence of the critical behavior on the…
We sketch a new framework for the analysis of disordered systems, in particular mean field spin glasses, which is variational in nature and within the formalism of classical thermodynamics. For concreteness, only the Sherrington-Kirkpatrick…
We describe the quantum phase transitions in the ferromagnetic Dicke-Ising model using a Landau theory approach. The theory quantitatively captures the change from a second- to a first-order transition between the normal and superradiant…
Monte Carlo study of the deconfined critical action phase diagram reveals a region where spinon deconfinement occurs through a weak first-order phase transition, in agreement with Ginzburg-Landau theory. Wilson renormalization argument in…
In the paper we present simple examples of linear random fields defined on $\ZZ^2$ and $\ZZ^3$ which exhibit the scaling transition phenomenon. These examples lead to more general definition of the scaling transition and allow to understand…