Related papers: Geometric Critical Exponents in Classical and Quan…
We find a series of topological phase transitions of increasing order, beyond the more standard second-order phase transition in a one-dimensional topological superconductor. The jumps in the order of the transitions depend on the range of…
An algorithm for optimizing the MERA tensor network in an infinite system is presented. Using this technique we compute the critical exponents of Ising and XXZ model.
The geometric phase provides important mathematical insights to understand the fundamental nature and evolution of the dynamic response in a wide spectrum of systems ranging from quantum to classical mechanics. While the concept of…
We devise a classical algorithm which efficiently computes the quantum expectation values arising in a class of continuous variable quantum circuits wherein the final quantum observable | after the Heisenberg evolution associated with the…
This essay addresses the issue of gravitational phase transitions in the early universe. We suggest that a second order phase transition observed in the Causal Dynamical Triangulations approach to quantum gravity may have a cosmological…
Classical phase transitions, like solid-liquid-gas or order-disorder spin magnetic phases, are all driven by thermal energy fluctuations by varying the temperature. On the other hand, quantum phase transitions happen at absolute zero…
We calculate the critical exponents of the chiral phase transition at nonzero temperature using the thermal and chiral susceptibilities. We show that within a class of confining Dyson-Schwinger equation (DSE) models the transition is mean…
Genetic algorithms based on natural selection and minimal fluctuations have been applied to model physical and biological systems. Critical exponents have been extracted via computational simulations of nucleation for colossal…
An investigation of the quantum phase transition in both discrete and continuum field Dicke models is presented. A series of anticrossing features following the criticality is revealed in the band of the field modes. Critical exponents are…
This article first gives a concise introduction to quantum phase transitions, emphasizing similarities with and differences to classical thermal transitions. After pointing out the computational challenges posed by quantum phase…
In this article we provide a review of geometrical methods employed in the analysis of quantum phase transitions and non-equilibrium dissipative phase transitions. After a pedagogical introduction to geometric phases and geometric…
We present large scale simulations of a stochastic sandpile model in two dimensions. We use moments analysis to evaluate critical exponents and finite size scaling method to consistently test the obtained results. The general picture…
The purpose of this article is to exploit the geometric structure of Quantum Mechanics and of statistical manifolds to study the qualitative effect that the quantum properties have in the statistical description of a system. We show that…
A quantum phase transition may occur in the ground state of a system at zero temperature when a controlling field or interaction is varied. The resulting quantum fluctuations which trigger the transition produce scaling behavior of various…
Bifurcations can cause dynamical systems with slowly varying parameters to transition to far-away attractors. The terms ``critical transition'' or ``tipping point'' have been used to describe this situation. Critical transitions have been…
Semilinear elliptic equations of the form $-\Delta u =\lambda|u|^{p-2}u- |u|^{q-2}u$ in bounded and unbounded domains are considered. In the plane of exponents $p\times q$, the so-called critical exponents curve is introduced which…
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 well known scaling laws relating critical exponents in a second order phase transition have been generalized to the case of an arbitrarily higher order phase transition. In a higher order transition, such as one suggested for the…
The introduction of a metric onto the space of parameters in models in Statistical Mechanics and beyond gives an alternative perspective on their phase structure. In such a geometrization, the scalar curvature, R, plays a central role. A…
If we admit that quantum mechanics (QM) is universal theory, then QM should contain also some description of classical mechanical systems. The presented text contains description of two different ways how the mathematical description of…