Directed polymer in a random potential in higher dimensions of up to d=10+1

초록

Directed polymer in a random potential is studied in high dimensions from d = 7 + 1 to d = 10 + 1. The standard deviation Delta E(t) of the lowest energy E(t) of the polymer grows with t, where t is the length of the polymer, and the growth exponent beta is estimated from the relation Delta E(t) similar to t ( beta ). The dynamic exponent z is calculated using the end-to-end distance Delta X(t) of the polymer that increases in time as Delta X(t) similar to t (1/z ). Our numerical results show that the upper critical dimension should be higher than d = 10 + 1. The energy distribution becomes more asymmetric and is farther away from the Gaussian distribution as the substrate dimension increases. So we speculate that there is no upper critical dimension of the Kardar-Parisi-Zhang equation.

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