The partition function of the four-vertex model in inhomogeneous external field and trace statistics
| Autor: | N M Bogoliubov, Cyril Malyshev |
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| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
Trace (linear algebra) General Physics and Astronomy FOS: Physical sciences 01 natural sciences 0103 physical sciences Vertex model Boundary value problem 0101 mathematics Condensed Matter - Statistical Mechanics Mathematical Physics Generating function (physics) Mathematics Partition function (quantum field theory) Nonlinear Sciences - Exactly Solvable and Integrable Systems Statistical Mechanics (cond-mat.stat-mech) Plane (geometry) 010102 general mathematics Mathematical analysis Statistical and Nonlinear Physics Mathematical Physics (math-ph) Enumerative combinatorics Connection (mathematics) Modeling and Simulation 010307 mathematical physics Exactly Solvable and Integrable Systems (nlin.SI) |
| DOI: | 10.48550/arxiv.2011.10200 |
| Popis: | The exactly solvable four-vertex model with the fixed boundary conditions in the presence of inhomogeneous linearly growing external field is considered. The partition function of the model is calculated and represented in the determinantal form. The established connection with the boxed plane partitions allows us to calculate the generating function of plane partitions with the fixed sums of their diagonals. The obtained results are another example of the connection of integrable models with the enumerative combinatorics. Comment: 18 pages, 6 figures. arXiv admin note: text overlap with arXiv:0711.0030 |
| Databáze: | OpenAIRE |
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