Completeness of classical ${\varphi }^4$ theory on 2D lattices

Abstract

We formulate a quantum formalism for the statistical mechanical models of discretized field theories on lattices and then show that the discrete version of ${\varphi }^4$ 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.

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

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Cited by in corpus (9)

• Simple universal models capture all classical spin physics
• Universal Quantum Hamiltonians
• Dual correspondence between classical spin models and quantum CSS states
• An algorithmic proof for the completeness of two-dimensional Ising model
• Phase transition in a noisy Kitaev toric code model
• Translationally invariant universal classical Hamiltonians
• A quantum information approach to statistical mechanics
• Noisy Toric code and random bond Ising model: The error threshold in a dual picture
• Systematic study of the completeness of two-dimensional classical ${\varphi }^4$ theory