Abstract The Onsager relations are discussed and it is suggested that they should be interpreted as there a frame of reference where all the transport processes independent. concepts illustrated with isobarothermal diffusion in simple metallic phases well complex ionic systems. A transformation from lattice-fixed to number-fixed gives Kirkendall effect cross effect.

The liquid crystal phase transitions for a classical uid mixture of hard ellip-soids with aspect ratios 10 : 1 and 1 : 10, and equal volume, has been studied at two compositions using Onsager theories and by computer simulation. The original Onsager form of the Helmholtz free energy contains the second virial coeecient, but the eeect of higher virial coeecients may be taken into account indirec...

We demonstrate that the τ (j)-matrices in the superintegrable chiral Potts model possess the Onsager algebra symmetry for their degenerate eigenvalues. The Fabricius-McCoy comparison of functional relations of the eight-vertex model for roots of unity and the superintegrable chiral Potts model has been carefully analyzed by identifying equivalent terms in the corresponding equations, by which w...

The universality class, even the order of the transition, of the two-dimensional Ising model depends on the range and the symmetry of the interactions (Onsager model, Baxter-Wu model, Turban model, etc.), but the critical temperature is generally the same due to self-duality. Here we consider a sudden change in the form of the interaction and study the nonequilibrium critical dynamical properti...

We study Onsager’s model of nematic phase transitions with orientation parameter on a sphere. We consider two interaction potentials: the antisymmetric (with respect to orientation inversion) dipolar potential and symmetric Maier-Saupe potential. We obtain a complete classification and explicit expressions of all critical points, analyze their stability, and construct the corresponding bifurcat...

This paper presents the results of a theoretical study of the kinetics of atomic and ionic transport via interstitial defects for a particular model in which interstitial pairing occurs. These are compatible with the phenomenological equations suggested by the thermodynamics of irreversible processes. The Onsager reciprocal relation is verified and the forms of the phenomenological coefficients...

The goal of this experiment was to create Monte Carlo simulations of the 1D and 2D Ising model. To accomplish this the Metropolis algorithm was implemented in MATLAB. The dependence of magnetization on temperature with and without an external field was calculated, as well as the dependence of the energy, specific heat, and magnetic susceptibility on temperature. The results of the 2D simulation...

We investigate zero-field Ising models on periodic approximants of planar quasiperiodic tilings by means of partition function zeros and high-temperature expansions. These are obtained by employing a determinant expression for the partition function. The partition function zeros in the complex temperature plane yield precise estimates of the critical temperature of the quasiperiodic model. Conc...

An extension of the "prior density for path" (Onsager-Machlup functional) is defined and shown to exist for Gaussian fields generated by solutions of elliptic PDE's driven by white noise. This functional is then used to define and solve the MAP estimation of such fields observed via nonlinear noisy sensors. Existence results and a representation of the estimator are derived for this model. AMS ...