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Upper bounds to free energies by renormalization group methods

M N Barber

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The use of variational approximations in the study and application of renormalization groups is discussed. In particular, a simple approximation is derived which yields an upper bound to the free energy of Ising models on d-dimensional lattices. The optimal transformation, which yields the least upper bound, is determined analytically. The criterion proposed by Kadanoff (1975) to determine the 'best' approximation to the fixed point is found to fail in this case. The reasons for this failure and several of the basic problems posed by variational approximations are discussed.


PACS

05.70.Ce Thermodynamic functions and equations of state

05.10.Cc Renormalization group methods

05.50.+q Lattice theory and statistics (Ising, Potts, etc.)

MSC

82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs

82B28 Renormalization group methods (See also 81T17)

82B30 Statistical thermodynamics (See also 80-XX)

Subjects

Computational physics

Statistical physics and nonlinear systems

Dates

Issue 7 (July 1977)



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