*Barry M. McCoy*

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199556632
- eISBN:
- 9780191723278
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199556632.003.0009
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter presents the results of high temperature series expansions for classical n component spin models with nearest neighbor interactions for two and three dimensions. In dimension three this ...
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This chapter presents the results of high temperature series expansions for classical n component spin models with nearest neighbor interactions for two and three dimensions. In dimension three this data is used to estimate critical exponents. In dimension two the three-component model exhibits what in field theory is called ‘asymptotic freedom’ where the critical temperature is at T = 0. The corresponding analysis is done for the quantum Heisenberg model and universality with respect to the quantum spin is evaluated. A discussion of the relation between statistical mechanics and quantum field theory is given.Less

This chapter presents the results of high temperature series expansions for classical *n* component spin models with nearest neighbor interactions for two and three dimensions. In dimension three this data is used to estimate critical exponents. In dimension two the three-component model exhibits what in field theory is called ‘asymptotic freedom’ where the critical temperature is at *T* = 0. The corresponding analysis is done for the quantum Heisenberg model and universality with respect to the quantum spin is evaluated. A discussion of the relation between statistical mechanics and quantum field theory is given.

*Tadeusz Balaban, Joel Feldman, Horst Knörrer, and Eugene Trubowitz*

- Published in print:
- 2012
- Published Online:
- September 2012
- ISBN:
- 9780199652495
- eISBN:
- 9780191741203
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199652495.003.0002
- Subject:
- Physics, Atomic, Laser, and Optical Physics

This chapter is concerned with the first, relatively small, step in a program whose long-term goal is the mathematically rigorous construction of a standard model of a gas of bosons. Even this first ...
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This chapter is concerned with the first, relatively small, step in a program whose long-term goal is the mathematically rigorous construction of a standard model of a gas of bosons. Even this first step is too long and complicated to present completely. Instead it is outlined, with a couple of the tools employed being highlighted. Those tools tend to crop up quite commonly in constructions of quantum field theories and many-body models.Less

This chapter is concerned with the first, relatively small, step in a program whose long-term goal is the mathematically rigorous construction of a standard model of a gas of bosons. Even this first step is too long and complicated to present completely. Instead it is outlined, with a couple of the tools employed being highlighted. Those tools tend to crop up quite commonly in constructions of quantum field theories and many-body models.