Exact Spectral Dimension of the Random Surface

Abstract

We propose a new method of the analytical computation of the spectral dimension which is based on the equivalence of the random walk and the q-state Potts model with non-zero magnetic field in the limit $q\to 0$. Calculating the critical exponent of the magnetization of this model on the dynamically triangulated random surface by means of a matrix model technique we obtain that the spectral dimension of this surface is equal to two.

harvmac, 14 pages, 3 figures

References in corpus (2)

• Laplacian spectra of complex networks and random walks on them: Are scale-free architectures really important?
• The spectral dimension of generic trees