Macroscopic Limit of a Bipartite Curie–Weiss Model: A Dynamical Approach

We analyze the Glauber dynamics for a bi-populated Curie–Weiss model. We obtain the limiting behavior of the empirical averages in the limit of infinitely many particles. We then characterize the phase space of the model in absence of magnetic field and we show that several phase transitions in the inter-groups interaction strength occur.     

Zero-Temperature Dynamics in the Dilute Curie–Weiss Model

We consider the Ising model on a dense Erd?s–Rényi random graph, \({\mathcal {G}}(N,p)\), with \(p>0\) fixed—equivalently, a disordered Curie–Weiss Ising model with \(\hbox {Ber}(p)\) couplings—at zero temperature. The disorder may induce local energy minima in addition to the two uniform ground states. In this paper we prove that, starting from a typical initial configuration, the zero-temperature dynamics avoids all such local minima and absorbs into a predetermined one of the two uniform ground states. We relate this to the local MINCUT problem on dense random graphs; namely with high probability, the greedy search for a local MINCUT of \({\mathcal {G}}(N,p)\) with \(p>0\) fixed, started from a uniform random partition, fails to find a non-trivial cut. In contrast, in the disordered Curie–Weiss model with heavy-tailed couplings, we demonstrate that zero-temperature dynamics has positive probability of absorbing in a random local minimum different from the two homogenous ground states.     

Microcanonical Analysis of the Curie–Weiss Anisotropic Quantum Heisenberg Model in a Magnetic Field

The anisotropic quantum Heisenberg model with Curie-Weiss-type interactions is studied analytically in several variants of the microcanonical ensemble. (Non)equivalence of microcanonical and canonical ensembles is investigated by studying the concavity properties of entropies. The microcanonical entropy \(s(e,\varvec{m})\) is obtained as a function of the energy \(e\) and the magnetization vector \({\varvec{m}}\) in the thermodynamic limit. Since, for this model, \(e\) is uniquely determined by \({\varvec{m}}\) , the same information can be encoded either in \(s(\varvec{m})\) or \(s(e,m_1,m_2)\) . Although these two entropies correspond to the same physical setting of fixed \(e\) and \({\varvec{m}}\) , their concavity properties differ. The entropy \(s_{{\varvec{h}}}(u)\) , describing the model at fixed total energy \(u\) and in a homogeneous external magnetic field \({\varvec{h}}\) of arbitrary direction, is obtained by reduction from the nonconcave entropy \(s(e,m_1,m_2)\) . In doing so, concavity, and therefore equivalence of ensembles, is restored. \(s_{{\varvec{h}}}(u)\) has nonanalyticities on surfaces of co-dimension 1 in the \((u,\varvec{h})\) -space. Projecting these surfaces into lower-dimensional phase diagrams, we observe that the resulting phase transition lines are situated in the positive-temperature region for some parameter values, and in the negative-temperature region for others. In the canonical setting of a system coupled to a heat bath of positive temperatures, the nonanalyticities in the microcanonical negative-temperature region cannot be observed, and this leads to a situation of effective nonequivalence even when formal equivalence holds.     

Fluctuation of the Free Energy of Sherrington–Kirkpatrick Model with Curie–Weiss Interaction: The Paramagnetic Regime

Journal of Statistical Physics - We consider a spin system containing pure two spin Sherrington–Kirkpatrick Hamiltonian with Curie–Weiss interaction. The model where the spins are...     

A Conditional Curie–Weiss Model for Stylized Multi-group Binary Choice with Social Interaction

This paper proposes a conditional Curie–Weiss model as a model for decision making in a stylized society made up of binary decision makers that face a particular dichotomous choice between two options. Following Brock and Durlauf (Discrete choice with social interaction I: theory, 1955), we set-up both socio-economic and statistical mechanical models for the choice problem. We point out when both the socio-economic and statistical mechanical models give rise to the same self-consistent equilibrium mean choice level(s). Phase diagram of the associated statistical mechanical model and its socio-economic implications are discussed.     

Manifestation of Curie–Weiss law for optical phase transition

Considerable slowing down is observed for both the temporal development of the coherent oscillation slightly above the threshold and the refractive index grating decay slightly below the threshold for a semilinear photorefractive oscillator with two counter-propagating pump waves. It is shown that in the vicinity of the threshold the reciprocal characteristic time is a linear function of deviation from the threshold coupling strength. This behaviour is similar to an empirical Curie–Weiss law and points to the analogy of the oscillation threshold to a second-order phase transition. Received: 2 April 2001 / Revised version: 23 August 2001 / Published online: 7 November 2001     

The Curie–Weiss model with Complex Temperature: Phase Transitions

We study the partition function of the Curie–Weiss model with complex temperature, and partially describe its phase transitions. As a consequence, we obtain information on the locations of zeros of the partition function (the Fisher zeros).     

A Curie–Weiss theory of the continuum Widom–Rowlinson model

A version of the continuum Widom–Rowlinson model is introduced and studied. It is a two-component gas of point particles placed in ${\mathbf{R}}^d$ in which like particles do not interact and unlike particles contained in a given vessel of volume V repel each other with intensity $a/V$. This model is thermodynamically equivalent to a one-component gas with multi-particle interaction. For both models, a rigorous theory of a phase transition is presented and the ways of its construction in the framework of the grand canonical formalism are outlined.     

Dissipation of System and Atom in Two-Photon Jaynes–Cummings Model with Degenerate Atomic Levels

A method of perturbative expansion of master equation is employed to study the dissipative properties of system and of atom in the two-photon Jaynes–Cummings model (JCM) with degenerate atomic levels. The numerical results show that the degeneracy of atomic levels prolongs the period of entanglement between the atom and the field. The asymptotic value of atomic linear entropy is apparently increased by the degeneration. The amplitude of local entanglement and disentanglement is suppressed. The better the initial coherence property of the degenerate atom, the larger the coherence loss.     

On the Interplay of Magnetic and Molecular Forces in Curie–Weiss Ferrofluid Models

We consider a mean-field continuum model of classical particles in R ^d with Ising or Heisenberg spins. The interaction has two ingredients, a ferromagnetic spin coupling and a spin-independent molecular force. We show that a feedback between these forces gives rise to a first-order phase transition with simultaneous jumps of particle density and magnetization per particle, either at the threshold of ferromagnetic order or within the ferromagnetic region. If the direct particle interaction alone already implies a phase transition, then the additional spin coupling leads to an even richer phase diagram containing triple (or higher order) points.     

An Asymptotic Limit of a Navier–Stokes System with Capillary Effects

A combined incompressible and vanishing capillarity limit in the barotropic compressible Navier–Stokes equations for smooth solutions is proved. The equations are considered on the two-dimensional torus with well prepared initial data. The momentum equation contains a rotational term originating from a Coriolis force, a general Korteweg-type tensor modeling capillary effects, and a density-dependent viscosity. The limiting model is the viscous quasi-geostrophic equation for the “rotated” velocity potential. The proof of the singular limit is based on the modulated energy method with a careful choice of the correction terms.     

Deformed Potential Energy of ^263Db in a Generalized Liquid Drop Model

The macroscopic deformed potential energy for super-heavy nuclei ^263 Db, which governs the entrance and alphadecay channels, is determined within a generalized liquid drop model (GLDM). A quasi-molecular shape is as-sumed in the GLDM, which includes volume-, surface-, and Coulomb-energies, proximity effects, mass asymmetry,and an accurate nuclear radius. The microscopic single particle energies are derived from a shell model in anaxially deformed Woods-Saxon potential with a quasi-molecular shape. The shell correction is calculated by theStrutinsky method. The total deformed potential energy of a nucleus can be calculated by the macro-microscopicmethod as the summation of the liquid-drop energy and the Strutinsky shell correction. The theory is appliedto predict the deformed potential energy of the experiment ^22Ne ^241Am→^263Db^*→^259Db 4n, which wasperformed on the Heavy Ion Accelerator in Lanzhou. It is found that the neck in the quasi-molecular shape isresponsible for the deep valley of the fusion barrier due to the shell corrections. In the cold fusion path, thedouble-hump fusion barrier is predicted by the shell correction and complete fusion events may occur.     

The Phase Structure of a Generalized Gross–Neveu Model in (2+1)-Dimensional Space–Time

The phase structure of a (2+1)-dimensional Gross–Neveu model with four different channels of fermion–antifermion interaction, and, correspondingly, four different coupling constants, is studied. It is shown that the model describes five different phases of the interaction of planar fermions in which either spatial parity or chiral symmetry can be broken. The existence of a phase that is characterized by simultaneous spontaneous breaking of both these symmetries that was not observed earlier in such models is demonstrated.     

Self-dual Non-topological Vortices in a Maxwell–Chern–Simons Model with Non-minimal Coupling

We prove existence results for the self-dual non-topological solutions in a Maxwell–Chern–Simons model with non-minimal coupling by using the perturbation argument. We also study the structure of radially symmetric non-topological solutions.     

Flocking of the Motsch–Tadmor Model with a Cut-Off Interaction Function

In this paper, we study the flocking behavior of the Motsch–Tadmor model with a cut-off interaction function. Our analysis shows that connectedness is important for flocking of this kind of model. Fortunately, we get a sufficient condition imposed only on the model parameters and initial data to guarantee the connectedness of the neighbor graph associated with the system. Then we present a theoretical analysis for flocking, and show that the system achieves consensus at an exponential rate.     

Traveling Waves and Structures of a Film Flow with Phase Transitions in the Nakoryakov–Ostapenko–Bartashevich Model

To describe the motion of the film flowing downward the vertical wall in the mode of condensation or evaporation into the surrounding space, the model proposed in [1] is used. It is reduced to one equation for the film thickness. The model comprises two governing parameters. The first one is proportional to the difference in the wall temperature, assumed to be constant, and the saturation temperature, and the second is proportional to the surface tension coefficient. In a series of publications [1–4] the authors studied solutions of thementioned equation at zero surface tension. Their characteristic feature is the presence of strong and weak discontinuities of layer thickness. In this paper we studied the regularizing effect of surface tension on the film flow structure with phase transitions. Numerical and asymptotic analysis of the resulting structures is carried out. Also, the case where the wall temperature is an arbitrary function of time is considered.     

Deformed Potential Energy of Super Heavy Element Z = 120 in a Generalized Liquid Drop Model

The macroscopic deformed potential energy for super-heavy elements Z=120 is determined within a generalized liquid drop model (GLDM). The shell correction is calculated with the Strutinsky method and the microscopic single particle energies are derived from the shell model in an axially deformed Woods-Saxon potential with the same quasi-molecular shape. The total potential energy of a nucleus is calculated by the macro-microscopic method as the summation of the liquid-drop energy and the Strutinsky shell correction. The theory is adopted to describe the deformed potential energies in a set of cold reactions. The neck in the quasi-molecular shape is responsible to the deep valley of the fusion barrier due to shell corrections. In the cold fusion path, the double-hump fusion barrier is predicted by the shell correction and complete fusion events may occur. The results show that some of projectile-target combinations in the entrance channel, such as ^50Ca ^252Fm→120 and 58Fe 244 pu→^302 120 , favour the fusion reaction, which can be considered as candidates for the synthesis of super heavy nuclei Z=120 and the former might be the best cold fusion reaction to produce the nucleus ^302 120among them.