Critical behavior of target space mean field theory

Details Critical behavior of target space mean field theory Critical behavior of target space mean field theory

1993-07-19

arxiv.org/abs/hep-th/9307120v1

Mod. Phys. Lett. A8 (1993) 2703-2714

Physics

High Energy Physics

High Energy Physics - Theory

12 pp., TeX + harvmac + epsf, PUPT-1412

Scientific paper

10.1142/S0217732393003093

Recently, the free energy of the target space mean field (TSMF) matrix model has been calculated in the low temperature phase, order-by-order in a low temperature expansion. The TSMF model is a matrix model whose discrete target space has an infinite coordination number, and whose free energy assumes a universal form, corresponding to baby universes joined into a tree. Here the free energy is summed to all orders, and expressed through a transcendental algebraic equation, using which we analyze the critical phenomena that occur in the TSMF model. There are two critical curves, at which the matter and the geometry become critical, and for which the critical exponents are alpha = 1/2 and gamma_str = -1/2, respectively. There is a bicritical point where the curves meet, at which gamma_str = +1/3.

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