The Ising Model on Random Planar Lattice: The Structure of Phase Transition and the Exact Critical Exponents

Jul, 1986
6 pages
Published in:
  • Phys.Lett.B 186 (1987) 379
  • Published: 1987
Report number:
  • SPI-MOSCOW-1154

Citations per year

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Abstract: (Elsevier)
We investigate the critical properties of a recently proposed exactly soluble Ising model on a planar random dynamical lattice representing a regularization of the zero-dimensional string with internal fermions. The sum over all lattices gives rise to a new quantum degree of freedom - fluctuation of the metric. The whole system of critical exponents is found: α = −1, β = 1 2 , γ = 2, δ = 5, ν · D = 3. To test the universality we have used the planar graphs with the coordination number equal to 4 (θ 4 theory graphs) as well as with the equal to 3 (θ 3 theory graphs or triangulations). The critical exponents coincide for both cases.
  • STATISTICAL MECHANICS: ISING
  • MAGNETIC FIELD
  • STATISTICAL MECHANICS: CRITICAL PHENOMENA
  • LATTICE FIELD THEORY: RANDOM LATTICE