Gaussian phase transitions

Consider simulating a system m the canonical ensemble, close to a first-order phase transition. In one phase, is essentially a Gaussian centred around a value j, while in the other phase tlie peak is around Ejj. 

Far from the transition, one or other of these will apply. Close to the phase transition we will see contributions from both Gaiissians, and a double-peaked distribution. The weight of each Gaussian changes as the temperature is varied. Thus, a smooth... 

In the case of Gaussian and uniform distributions of the adsorption energy, the smearing of the phase transition region in the the first as well as higher layers was observed. Thus, insead of vertical jumps, the adsorption isotherms exhibited only finite slope even at quite low temperatures. This result is consistent with the predictions of Dash and Puff [32]. 

In the original MIT bag model the bag constant B 55 MeV fm-3 is used, while values B 210 MeV fm-3 are estimated from lattice calculations [34], In this sense B can be considered as a free parameter. We found, however, that a bag model involving a constant (density independent) bag parameter B, combined with our BHF hadronic EOS, will not yield the required phase transition in symmetric matter at pr 6po 1/fm3 [28]. This can only be accomplished by introducing a density dependence of the bag parameter. (The dependence on asymmetry is neglected at the current level of investigation). In practice we use a Gaussian parameterization,... 

Figure 3. Phase diagrams for different form-factor models Gaussian (solid lines), Lorentzian a = 2 (dashed lines) and NJL (dash-dotted). In /3-equilibrium, the colorsuperconducting phase does not exist for Co Gi. In the inset we show for the Gaussian model the comparison of the numerical result with the modified BCS formula Tf = 0.57 A(T = 0, fiq) g(Hq) for the critical temperature of the superconducting phase transition.

We have investigated the influence of diquark condensation on the thermodynamics of quark matter under the conditions of /5-equilibrium and charge neutrality relevant for the discussion of compact stars. The EoS has been derived for a nonlocal chiral quark model in the mean field approximation, and the influence of different form-factors of the nonlocal, separable interaction (Gaussian, Lorentzian, NJL) has been studied. The model parameters are chosen such that the same set of hadronic vacuum observable is described. We have shown that the critical temperatures and chemical potentials for the onset of the chiral and the superconducting phase transition are the lower the smoother the momentum dependence of the interaction form-factor is. 

Rusakov 107 108) recently proposed a simple model of a nematic network in which the chains between crosslinks are approximated by persistent threads. Orientional intermolecular interactions are taken into account using the mean field approximation and the deformation behaviour of the network is described in terms of the Gaussian statistical theory of rubber elasticity. Making use of the methods of statistical physics, the stress-strain equations of the network with its macroscopic orientation are obtained. The theory predicts a number of effects which should accompany deformation of nematic networks such as the temperature-induced orientational phase transitions. The transition is affected by the intermolecular interaction, the rigidity of macromolecules and the degree of crosslinking of the network. The transition into the liquid crystalline state is accompanied by appearence of internal stresses at constant strain or spontaneous elongation at constant force. 

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