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91.
Michael K. -H. Kiessling 《Journal of statistical physics》1990,59(5-6):1157-1186
The canonical equilibrium measure of classical two-component Coulomb matter with regularized interactions is analyzed in a finite volume. It is shown that, in the mean-field regime, the one-particle density is inhomogeneous on a new characteristic length scale inh. For a system ofN positive andN negative particles, inh and the characteristic length scale of correlations corr (=Debye screening length) are related via inh=(2N)1/2 corr. The major conceptual conclusion that is drawn from this is that one needs two nontrivial complementary thermodynamic limits to define the equilibrium thermodynamics of two-component Coulomb systems. One of them is the standard thermodynamic limit (infinite volume), where one takesN, corr fixed. Its complementary limit is characterized byN, inh fixed, and is a finite-volume inhomogeneous mean-field limit. The most prominent new feature in the mean-field thermodynamic limit, which is absent in the standard thermodynamic limit, is an anomalous first-order phase transition where the Coulomb system explodes or implodes, respectively. The phase transition is connected with the existence of a metastable plasma phase far below the ionization temperature. 相似文献
92.
For an exactly soluble classical spin model with long-range inhomogeneous coupling it is proved that in the absence of external magnetic field the free energy is aC
function of the temperature at the critical point. 相似文献
93.
Tom Kennedy 《Journal of statistical physics》1990,59(1-2):195-220
A fixed-point equation on an infinite-dimensional space is proposed as an alternative to the usual definition of the infinite-volume limit in discrete lattice spin systems in the high-temperature phase. It is argued heuristically that the free energy and correlation functions one obtains by solving this equation agree with the usual definitions of these quantities. A theorem is then proved that says that if a certain finite-volume condition is satisfied, then this fixed-point equation has a solution and the resulting free energy is analytic in the parameters in the Hamiltonian. For particular values of the temperature this finite-volume condition may be checked with the help of a computer. The two-dimensional Ising model is considered as a test case, and it is shown that the finite-volume condition is satisfied for0.77
critical. 相似文献
94.
P. J. Forrester 《Journal of statistical physics》1988,51(3-4):457-479
The Coulomb system consisting of an equal number of positive and negative charged rods confined to a one-dimensional lattice is studied. The grand partition function can be calculated exactly at two values of the coupling constant=q
2/k
B
T (q denoting the magnitude of the charges). The exact results lead to the conjecture that in the complex scaled fugacity plane, all the zeros of the grand partition function lie on the negative real axis for<2, on the point=–1 for=2, and on the unit circle for>2. In addition, for>4, we conjecture in general and prove at=4 that the zeros pinch the real axis in the thermodynamic limit, with an essential singularity in the pressure at the reduced density 1/2. 相似文献
95.
P. G. J. van Dongen 《Journal of statistical physics》1989,54(1-2):221-271
A general method is used for describing reaction-diffusion systems, namely van Kampen's method of compounding moments, to study the spatial fluctuations in reaction-limited aggregation processes. The general formalism used here and in subsequent publications is developed. Then a particular model is considered that is of special interest, since it describes the occurrence of a phase transition (gelation). The corresponding rate constants for the reaction between two clusters of sizei and sizej areK
ij=ij (i, j=1, 2,). For thediffusion constants D
j of clusters of sizej the following class of models is considered:D
j=D if 1Js andD
j=0 ifj>s. The casess= ands< are studied separately. For the models= the equal-time and the two-time correlation functions are calculated; this modelbreaks down at the gel point. The breakdown is characterized by a divergence of the density fluctuations, and is caused by the large mobility of large clusters. For all models withs< the density fluctuations remain finite att
c, and the equal-time correlation functions in the pre- and in the post-gel stage are calculated. Many explicit and asymptotic results are given. From the exact solution the upper critical dimension in this gelling model isd
c=2. 相似文献
96.
97.
98.
Summary The equation for the potential energy of interactions established for gas-liquid chromatography has been confirmed in reversed phase liquid chromatography. Equations derived for molecular polarizabilities of PAHs and their retention data have very high correlation coefficients. The results indicate that the inductive effect between solute and stationary phase is the main one and the dispersive effect is very small compared with the inductive effect but its contribution increases with the carbon chain length of the stationary phase. 相似文献
99.
Summary Further to Gilpin's observations in liquid chromatography of the irreversible transformation of alkyl grafts, following the replacement of an organic mobile phase by an aqueous one, we describe some gas chromatographic experiments which lead to similar (log Vs, I/T) plots, as a consequence of the same solvent release process.We use paraffin films on siliceous supports or hydroxylated liquid substrates or C22-alkyl bonded silica. These experiments demonstrate that this irreversible transition and the melting-like reversible transition are completely different phenomena. They confirm the existence of at least three kinds of monomeric alkyl films. 相似文献
100.