Related papers: Mean-field ansatz for topological phases with stri…
We review a recent approach to the mean-field limits in neural networks that takes into account the stochastic nature of input current and the uncertainty in synaptic coupling. This approach was proved to be a rigorous limit of the network…
In a previous study we developed a mean-field theory of dynamical transitions for the totally-asymmetric simple-exclusion process (TASEP) with open boundaries and Langmuir kinetics, in the so-called balanced regime, characterized by equal…
We construct an explicitly solvable Landau mean-field theory for volume phase transitions of confined or fixed ions driven by relative concentrations of divalent and monovalent counterions. Such phase transitions have been widely studied in…
The eigenvalue structure of the quantum transfer matrix is known to encode essential information about the elementary excitations. Here we study transfer matrices of quantum states in a topological phase using the tensor network formalism.…
For algorithms based on interacting particle systems that admit a mean-field description, convergence analysis is often more accessible at the mean-field level. In order to transfer convergence results obtained at the mean-field level to…
We study a class of Markov chains that describe reversible stochastic dynamics of a large class of disordered mean field models at low temperatures. Our main purpose is to give a precise relation between the metastable time scales in the…
We point out a new mechanism which can lead to mean field type behaviour in nonequilibrium critical phenomena. We demonstrate this mechanism on a two-dimensional model which can be understood as a stochastic and non-conservative version of…
It is known that string theory compactifications leading to low energy effective theories with different chiral matter content ({\it e.g.} different numbers of standard model generations) are connected through phase transitions, described…
If the behavior of a system with many degrees of freedom can be captured by a small number of collective variables, then plausibly there is an underlying mean-field theory. We show that simple versions of this idea fail to describe the…
We show that the one loop amplitudes of open and closed string theory in a constant background two-form tensor field are characterized by an effective string tension larger than the fundamental string tension, and by the appearance of…
It is believed that, much like a cat's cradle, the cytoskeleton can be thought of as a network of strings under tension. We show that both regular and random bond-disordered networks having bonds that buckle upon compression exhibit a…
A mean field theory of the localization transition for bosonic systems is developed. Localization is shown to be sensitive to the distribution of the random site energies. It occurs in the presence of a triangular distribution, but not a…
Topological qauntum field theory(TQFT) is a very powerful theoretical tool to study topological phases and phase transitions. In $2+1$D, it is well known that the Chern-Simons theory captures all the universal topological data of…
We show under general assumptions that the mean-field approximation for quan- tum many-boson systems is correct. Our contribution unifies and improves on most of the known results. The proof uses general properties of quantization in…
In this paper, we explores the expressivity and trainability of the Fourier Neural Operator (FNO). We establish a mean-field theory for the FNO, analyzing the behavior of the random FNO from an edge of chaos perspective. Our investigation…
We address a recently introduced model describing a system of periodically coupled nonlinear phase oscillators submitted to multiplicative white noises, wherein a ratchet-like transport mechanism arises through a symmetry-breaking…
In coupled rotor models which describe identical rotating nuclei the nuclear spin states restrict the possible angular momenta of each molecule. There are two mean-field approaches to determining the orientational phase diagrams in such…
The majority-vote (MV) model is one of the simplest nonequilibrium Ising-like model that exhibits a continuous order-disorder phase transition at a critical noise. In this paper, we present a quenched mean-field theory for the dynamics of…
A quantum phase transition is usually achieved by tuning physical parameters in a Hamiltonian at zero temperature. Here, we demonstrate that the ground state of a topological phase itself encodes critical properties of its transition to a…
Nonequilibrium conditions fundamentally change how systems undergo phase separation. In systems with temperature gradients, attractive particles have been shown to form periodic patterns and steady convective currents, but a clear…