Topics in statistical mechanics

Technical Report · Tue May 01 00:00:00 EDT 1984

DOI:https://doi.org/10.2172/6810491· OSTI ID:6810491

Elser, V

This thesis deals with four independent topics in statistical mechanics: (1) the dimer problem is solved exactly for a hexagonal lattice with general boundary using a known generating function from the theory of partitions. It is shown that the leading term in the entropy depends on the shape of the boundary; (2) continuum models of percolation and self-avoiding walks are introduced with the property that their series expansions are sums over linear graphs with intrinsic combinatorial weights and explicit dimension dependence; (3) a constrained SOS model is used to describe the edge of a simple cubic crystal. Low and high temperature results are derived as well as the detailed behavior near the crystal facet; (4) the microscopic model of the lambda-transition involving atomic permutation cycles is reexamined. In particular, a new derivation of the two-component field theory model of the critical behavior is presented. Results for a lattice model originally proposed by Kikuchi are extended with a high temperature series expansion and Monte Carlo simulation. 30 references.

• Research Organization: Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
• DOE Contract Number: AC03-76SF00098
• OSTI ID: 6810491
• Report Number(s): LBL-17840; ON: DE84013246
• Resource Relation: Other Information: Thesis
• Country of Publication: United States
• Language: English

Related Subjects

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STATISTICAL MECHANICS
DIMERS
CHEMICAL BONDS
DIFFUSION
CRYSTALS
SURFACE PROPERTIES
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HEXAGONAL LATTICES
GAUSSIAN PROCESSES
HAMILTONIANS
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PARTITION FUNCTIONS
BOSE-EINSTEIN GAS
LATTICE FIELD THEORY
PHASE TRANSFORMATIONS
CRYSTAL LATTICES
CRYSTAL STRUCTURE
ELEMENTS
FIELD THEORIES
FLUIDS
FUNCTIONS
GASES
MATHEMATICAL OPERATORS
MECHANICS
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PHYSICAL PROPERTIES
QUANTUM FIELD THEORY
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