Completeness of classical $φ^4$ theory on 2D lattices

Details Completeness of classical $φ^4$ theory on 2D lattices Completeness of classical $φ^4$ theory on 2D lattices

2012-01-22

arxiv.org/abs/1201.4558v3

Phys. Rev. A 85, 032316 (2012)

Physics

Quantum Physics

20 pages, 8 figures, Accepted for publication in Physical Review A

Scientific paper

We formulate a quantum formalism for the statistical mechanical models of discretized field theories on lattices and then show that the discrete version of $\phi^4$ theory on 2D square lattice is complete in the sense that the partition function of any other discretized scalar field theory on an arbitrary lattice with arbitrary interactions can be realized as a special case of the partition function of this model. To achieve this, we extend the recently proposed quantum formalism for the Ising model \cite{quantum formalism} and its completeness property \cite{completeness} to the continuous variable case.

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