By Dr. David A. Lavis, Professor George M. Bell (auth.)
This two-volume paintings presents a complete research of the statistical mechanics of lattice versions. It introduces the reader to the most components in statistical mechanics and the speculation of part transitions. the improvement is equipped on an organization mathematical and actual foundation. quantity 1 includes an account of mean-field and cluster edition equipment effectively utilized in many functions in solid-state physics and theoretical chemistry in addition to an account of tangible effects for the Ising and six-vertex types and people derivable via transformation equipment. quantity 2 contains wide remedies of scaling thought, algebraic and real-space renormalization tools and the eight-vertex version. additionally it is an account of sequence equipment and a remedy of dimer assemblies.
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Additional info for Statistical Mechanics of Lattice Systems: Volume 1: Closed-Form and Exact Solutions
Sample text
4 for the spin-1 model. Since each site is occupied by a spin, Ising model partition functions are restricted in the sense of Sect. 4. 63), is invariant under the operation <1; -+ -
J, 2 , ... l" and -P. 92) the dimension of the region of coexistence is 'D(K,p) = 9"(K + 1,p) = K,- p + 2. 93) For two coexisting one-component phases 'D(1, 2) = 1 in agreement with the result obtained above for liquid-vapour equilibrium. Since 'D (K, p) 2: 0 we conclude that the largest number of phases of a K component system which can coexist is K + 2. There are exceptions to this, which arise when the phase diagram has some special symmetry. One of these is the triangular ferrimagnetic Ising model discussed in Sect.
Moreover, we shall see in Sect. 2. 7 that there is at least one case where the one-dimensional Ising model can be used as a simple model for certain aspects of a real physical system. For the Ising model it is useful to define the Boltzmann factors 3 = exp(1-C/T) . X= exp(J/T) , (2. 66) consists of a contribution -Jakak+l from each successive site pair (k,k + 1) . 77) {~} is independent of a. 74), the constant magnetic field configurational partition function for }( = 0 is given by (2. 78) {a , ~,-y , ...