We numerically exhibit two strange phenomena of finite-size fluctuation in thermal equilibrium of a paradigmatic long-range interacting system having a second-order phase transition. One is a nonclassical finite-size scaling at the critical point, which differs from the prediction by statistical mechanics. With the aid of this strange scaling, the scaling theory for infinite-range models conjec...

We study the quantum phase transition properties of a three-dimensional periodic array of Josephson junctions with charging energy that includes both the self and mutual junction capacitances. We use the phase fluctuation algebra between number and phase operators, given by the Euclidean group E2, and we effectively map the problem onto a solvable quantum generalization of the spherical model. ...

We investigate the spectral fluctuation properties of constrained ensembles of random matrices (defined by the condition that a number NQ of matrix elements vanish identically; that condition is imposed in unitarily invariant form) in the limit of large matrix dimension. We show that as long as NQ is smaller than a critical value (at which the quadratic level repulsion of the Gaussian unitary e...

The time evolution of an exactly solvable layered feedforward neural network with three-state neurons and optimizing the mutual information is studied for arbitrary synaptic noise (temperature). Detailed stationary temperature-capacity and capacity-activity phase diagrams are obtained. The model exhibits pattern retrieval, pattern-fluctuation retrieval and spin-glass phases. It is found that th...

We study the dynamics of ferromagnetic spin systems quenched from infinite temperature to their critical point. We show that these systems are aging in the long-time regime, i.e., their two-time autocorrelation and response functions and associated fluctuation-dissipation ratio are non-trivial scaling functions of both time variables. This is exemplified by the exact analysis of the spherical m...

We consider a mean-field dynamical urn model, defined by rules which give the rate at which a ball is drawn from an urn and put in another one, chosen amongst an assembly. At equilibrium, this model possesses a fluid and a condensed phase, separated by a critical line. We present an analytical study of the nonequilibrium properties of the fluctuating number of balls in a given urn, considering ...

Thermal composition fluctuations and the associated crossover from the 3D Ising to the isotropic Lifshitz universality class have been studied in a three component mixture made of a critical polymer blend and the corresponding diblock copolymer. The critical exponents were found to be appreciably larger than those of the 3D Ising, in agreement with expectations from the larger upper critical di...

We present a new mechanism of fluctuation-induced Nambu-Goldstone bosons in a scalar field theory of Higgs-Josephson systems. We consider a simple scalar field model with U(1) rotational symmetry. When there is an interaction which violates the rotational symmetry, the Nambu-Goldstone bosons become massive and massless bosons are concealed. We present a model where the massive boson becomes a m...

The successful development of an effective temperature would be an important step in the application of statistical mechanics principles to systems driven far from equilibrium. One direction that has shown promise is the use of fluctuation-dissipation relations. However, driven systems break time-reversal symmetry, and understanding the implications of this for fluctuation-dissipation relations...