English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The completeness of some classical statistical mechanical (SM) models is arecent result that has been developed by quantum formalism for the partitionfunctions. In this paper, we consider a 2D classical $\phi^4$ filed theorywhose completeness has been proved in [V. Karimipour and et al, Phys. Rev. A85, 032316]. We give a general systematic proof for the completeness of such amodel where, by a few simple steps, we show how the partition function of anarbitrary classical field theory can be derived from a 2D classical $\phi^4$model. To this end, we start from various classical field theories containingmodels on arbitrary lattices and also $U(1)$ lattice gauge theories. Then weconvert them to a new classical field model on a non-planar bipartite graphwith imaginary kinetic terms. After that, we show that any polynomial functionof the field in the corresponding Hamiltonian can approximately be converted toa $\phi^4$ term by adding enough numbers of vertices to the bipartite graph. Inthe next step, we give a few graphical transformations to convert the finalnon-planar graph to a 2D rectangular lattice. We also show that the number ofvertices which should be added grows polynomially with the number of verticesin the original model.

Systematic study of the completeness of two-dimensional classical $\phi^4$ theory