X iv :c on dm at /0 41 11 76 v1 [ co nd -m at .s ta tm ec h] 7 N ov 2 00 4 PARTITION FUNCTIONS FOR STATISTICAL MECHANICS WITH MICROPARTITIONS AND PHASE TRANSITIONS AJAY PATWARDHAN Physics department, St Xavier’s college, Mahapalika Marg , Mumbai 400001,India Visitor, Institute of Mathematical Sciences, CIT campus, Tharamani, Chennai, India [email protected] ABSTRACT The fundamentals of Statistic...

A practical version of the polynomial canonical formalism is developed for normal mesoscopic systems consisting of N independent electrons. Drastic simplification of calculations is attained by means of proper ordering excited states of the system. In consequence the exact canonical partition function can be represented as a series in which the first term corresponds to the ground state whereas...

For a thermal field theory formulated in the grand canonical ensemble, the distribution of the total momentum is an observable characterizing the thermal state. We show that its cumulants are related to thermodynamic potentials. In a relativistic system, for instance, the thermal variance of the total momentum is a direct measure of the enthalpy. We relate the generating function of the cumulan...

A multi-partition with evaluations is defined by two sets S and X, a collection P, . . . ,P of partitions of S and a function ψ : S → {0, 1} . To each partition P corresponds a person j who cannot distinguish between any two points belonging to the same member of P but can distinguish between different members of P. A cell of a multi-partition is a minimal subset C such that for all j the prope...

A bstract We study the Schur line defect correlation functions in $$ \mathcal{N} = 4 and 2 ∗ U( N ) super Yang-Mills (SYM) theory. find exact closed-form formulae of Wilson operators fundamental, antisymmetric symmetric representations via Fermi-gas method canonical grand ensembles. All correlators are shown to be expressible terms multiple series that generalizes Kronecker theta function. From...

A set partition of size n is a collection of disjoint blocks B1, B2, . . . , Bd whose union is the set [n] = {1, 2, . . . , n}. We choose the ordering of the blocks so that they satisfy minB1 < minB2 < · · · < minBd. We represent such a set partition by a canonical sequence π1, π2, . . . , πn, with πi = j if i ∈ Bj. We say that a partition π contains a partition σ if the canonical sequence of π...

A set partition of the set [n] = {1,. .. , n} is a collection of disjoint blocks B 1 , B 2 ,. .. , B d whose union is [n]. We choose the ordering of the blocks so that they satisfy min B 1 < min B 2 < · · · < min B d. We represent such a set partition by a canonical sequence π 1 , π 2 ,. .. , πn, with π i = j if i ∈ B j. We say that a partition π contains a partition σ if the canonical sequence...

The nonanalyticity and the sign problem in Z3-symmetric heavy quark model at low temperature are studied phenomenologically. For free quarks, is analyzed relation to zeros of grand canonical partition function. effective Polyakov-line (EPLM) strong coupling limit also considered as an phenomenological QCD with large mass temperature. We examine how EPLM approaches original one zero-temperature ...