Critical Dimensions of the Diffusion Equation
Abstract
We study the evolution of a random initial field under pure diffusion in various space dimensions. From numerical calculations we find that the persistence properties of the system show sharp transitions at critical dimensions d_{1}~=26 and d_{2}~=46. We also give refined measurements of the persistence exponents for low dimensions.
 Publication:

Physical Review Letters
 Pub Date:
 March 2001
 DOI:
 10.1103/PhysRevLett.86.2712
 arXiv:
 arXiv:condmat/0009365
 Bibcode:
 2001PhRvL..86.2712N
 Keywords:

 Condensed Matter  Statistical Mechanics;
 High Energy Physics  Lattice;
 High Energy Physics  Theory;
 Nonlinear Sciences  Cellular Automata and Lattice Gases;
 Physics  Atomic Physics
 EPrint:
 4 pages, 5 figures