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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
The q -state Potts Model: Partition functions and their zeros in the complex temperature- and q-plane

The q -state Potts Model: Partition functions and their zeros in the complex temperature- and q-plane

Klüpfel, Hubert

Paperback

Physics

ISBN10: 3656297398
ISBN13: 9783656297390
Publisher: Grin Verlag
Published: Mar 21 2014
Pages: 128
Weight: 0.39
Height: 0.30 Width: 5.83 Depth: 8.27
Language: English
Master's Thesis from the year 1999 in the subject Physics - Theoretical Physics, grade: 1,0, State University of New York at Stony Brook (Institute for Theoretical Physics), course: -, language: English, abstract: In this thesis results on the Partition function ZG(T, q) for the q-state Potts-Model on finite polygonal lattices G are presented. These are polynomials in a ≡ e- J and q. The first step is to calculate all the coefficients of ZG(a, q) using a transfer matrix method. The only points of non-analyticity are the zeros of the partition function; in the thermodynamic limit the complex temperature zeros form a continuous curve B via coalescence. This is the locus where the free energy is non-analytic. The zeros of Z(a, q) in the complex q-plane for finite a and in the complex a-plane for integer and non-integer values of q are plotted. For a = 0 the partition function reduces to the chromatic polynomial PG(q) of the graph and the zeros are called chromatic zeros. The behavior of those zeros as a increases from zero is investigated. As for complex temperature the zeros in q form a continuous curve in the thermodynamic limit. This is the locus where the limiting function WG(q) = limn→∞ PG(q)1/n is non-analytic. WG(q) is the ground state degeneracy and is connected to the ground state entropy via S0(G, q) = kB ln(WG(q)). Thus the characteristics of the zeros of q and a for finite lattices help to understand the properties of the model in the thermodynamic limit.

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