Even-visiting walks on random potentials

초록

The scaling properties of even-visiting walks on random potentials (EVWB.P) are presented. For a given random potential, the minimum energy path among even-visiting random walks (EVBW), which visit each site an even number of times, is found by an exact enumeration method, We measure the root mean square radius of gyration G(N) of such paths and show that the radius increases as G(AF) similar to N-alpha where N is the total number of steps. The measured "roughness" exponent alpha is close to 2/3: the value of the walks on random potential (WBP) without the constraint of even visit. We present an energy argument as to why EVWRP should have more similarities to WBP than EVMV.