Critical behavior in $c=1$ matrix model with branching interactions

Details Critical behavior in $c=1$ matrix model with branching interactions Critical behavior in $c=1$ matrix model with branching interactions

1994-03-16

arxiv.org/abs/hep-th/9403089v3

Mod.Phys.Lett. A9 (1994) 3149-3162

Physics

High Energy Physics

High Energy Physics - Theory

11pages. latex (The arguments in Discussions are corrected and more clarified! Several grammatical errors are corrected. And s

Scientific paper

10.1142/S0217732394002975

Motivated by understanding the phase structure of $d >1$ strings we investigate the $c=1$ matrix model with $g' (\tr M(t)^{2})^{2}$ interaction which is the simplest approximation of the model expected to describe the critical phenomena of the large-$N$ reduced model of odd-dimensional matrix field theory. We find three distinct phases: (i) an ordinary $c=1$ gravity phase, (ii) a branched polymer phase and (iii) an intermediate phase. Further we can also analyse the one with slightly generalized $ g^{(2)} (\frac{1}{N}\tr M(t)^{2})^{2} +g^{(3)} (\frac{1}{N}\tr M(t)^{2})^{3} + \cdots + g^{(n)} (\frac{1}{N}\tr M(t)^{2})^{n} $ interaction. As a result the multi-critical versions of the phase (ii) are found.

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