The spiralling self-avoiding walk and chaotic correlations

✍ Scribed by Muriel Nifle

• Publisher: Elsevier Science
• Year: 1992
• Tongue: English
• Weight: 245 KB
• Volume: 185
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/0378-4371(92)90450-5

✦ Synopsis

The spiralling self-avoiding lattice walk in a random environment is studied, The average size of an N-step walk is asymptotically proportional to N 1~2 log N with a coefficient that increases with the disorder.

A phase transition appears after scaling the temperature appropriately with system size. In the low-temperature phase the walk segments occupy a few low-energy positions, in the high-temperature phase they are effectively free. An analogy with the random energy model is poir~ted out.

The model also allows for a spin glass interpretation. The pair correlation varies chaotically with temperature both above and below the critical point.