{"product_id":"the-q-state-potts-model-partition-functions-and-their-zeros-in-the-complex-temperature-and-q-plane-von-hubert-klupfel","title":"The q -state Potts Model: Partition functions and their zeros in the complex temperature- and q-plane","description":"\u003cp\u003eMaster'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.\u003c\/p\u003e\u003cp\u003eThese 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.\u003c\/p\u003e\u003cp\u003eThe 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 äplane for integer and non¿integer values of q are plotted.\u003c\/p\u003e\u003cp\u003eFor a = 0 the partition function reduces to the chromatic polynomial PG(q) of the graph and the zeros are called chromatic zeros.\u003c\/p\u003e\u003cp\u003eThe behavior of those zeros as a increases from zero is investigated.\u003c\/p\u003e\u003cp\u003eAs 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)).\u003c\/p\u003e\u003cp\u003eThus the characteristics of the zeros of q and a for finite lattices help to understand the properties of the model in the thermodynamic limit.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783656297390\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9783656297390","offer_id":39432436908125,"sku":"9783656297390","price":47.95,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/adbef6b6-55ed-4c89-9d0a-60de9dd01597.jpg?v=1781410514","url":"https:\/\/shop.autorenwelt.de\/en\/products\/the-q-state-potts-model-partition-functions-and-their-zeros-in-the-complex-temperature-and-q-plane-von-hubert-klupfel","provider":"Autorenwelt Shop","version":"1.0","type":"link"}