Related papers: On the mean-field equations for ferromagnetic spin…
We give a comprehensive self-contained review on the rigorous analysis of the thermodynamics of a class of random spin systems of mean field type whose most prominent example is the Hopfield model. We focus on the low temperature phase and…
We consider two limiting regimes, the large-spin and the mean-field limit, for the dynamical evolution of quantum spin systems. We prove that, in these limits, the time evolution of a class of quantum spin systems is determined by a…
We consider properties of a two-dimensional electron system in a random magnetic field. It is assumed that the magnetic field not only influences orbital electron motion but also acts on the electron spin. For calculations, we suggest a new…
The mean field solution of the Ising model on a Barabasi-Albert scale-free network with ferromagnetic coupling between linked spins is presented. The critical temperature $T_c$ for the ferromagnetic to paramagnetic phase transition (Curie…
Collective ferromagnetic motion in a conducting medium is damped by the transfer of the magnetic moment and energy to the itinerant carriers. We present a calculation of the corresponding magnetization relaxation as a linear-response…
Here, we observe that mean-field game (MFG) systems admit a two-player infinite-dimensional general-sum differential game formulation. We show that particular regimes of this game reduce to previously known variational principles.…
The free energy of effective spin or "Polyakov line" models with a chemical potential, based on the U(N) group, does not depend on the chemical potential. In a mean field-inspired expansion, we show how the condition of unit determinant,…
The statement of the mean field approximation theorem in the mean field theory of Markov processes particularly targets the behaviour of population processes with an unbounded number of agents. However, in most real-world engineering…
We introduce a mean-field framework for the study of systems of interacting particles sharing a conserved quantity. The work generalises and unites the existing fields of asset-exchange models, often applied to socio-economic systems, and…
We consider a wide class of quantum spin systems obtained by adding a transverse field to a classical Hamiltonian. We give explicit high-temperature conditions which guarantee exponential decay of correlations. A stochastic-geometric…
In this review article we briefly summarize the main experimental properties of (III,Mn)V ferromagnets and outline several different but related approaches that have been explored in an effort to gain insight into these materials. The main…
We present a spin model, namely, the Kitaev model augmented by a loop term and perturbed by an Ising Hamiltonian and show that it exhibits both confinement-deconfinement transitions from spin liquid to…
Recent work on the zero temperature phases and phase transitions of strongly random electronic system is reviewed. The transition between the spin glass and quantum paramagnet is examined, for both metallic and insulating systems. Insight…
We study a block spin mean-field Ising model, i.e. a model of spins in which the vertices are divided into a finite number of blocks with each block having a fixed proportion of vertices, and where pair interactions are given according to…
A mechanism for ferrimagnetism in (1+1)-dimensions is discussed. The ferrimagnetism is cased by interactions described by operators with non-zero conformal spin. Such interactions appear in such problems as the problem of tunneling between…
Here we examine O(n) systems with arbitrary two spin interactions (of unspecified range) within a general framework. We shall focus on translationally invariant interactions. In the this case, we determine the ground states of the $O(n \ge…
Few years ago, application of the mean field Bethe scheme on a given system was shown to produce a systematic change of the system intrinsic symmetry. For instance, once applied on a ferromagnet, individual spins are no more equivalent.…
The theory of mean field games aims at studying deterministic or stochastic differential games (Nash equilibria) as the number of agents tends to infinity. Since very few mean field games have explicit or semi-explicit solutions, numerical…
We study analytically the equilibrium properties of the spherical hierarchical model in the presence of random fields. The expression for the critical line separating a paramagnetic from a ferromagnetic phase is derived. The critical…
The large amounts of data from molecular biology and neuroscience have lead to a renewed interest in the inverse Ising problem: how to reconstruct parameters of the Ising model (couplings between spins and external fields) from a number of…