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Tuning the trip to KPZ asymptopia

Timothy Halpin-Healy·Rachayl Novoseller
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Abstract

Because of a close blood relationship between directed percolation & directed polymers in random media, the latter's journey to asymptotic scaling can be greatly retarded by an uninformed choice of departure point; i.e., the bare-bond PDF employed in the transfer matrix study. Bisecting a gaussian noise distribution, examining DPRM scaling for left & right halves separately, and comparing results against the full PDF, reveals in the simplest possible manner the essence of this dilemma. Paradoxically, when the bare-bond PDF possesses a relative shortage [left demi-gaussian], rather than abundance [right demi-gaussian] of low energy bonds, much better scaling is achieved. This finding is somewhat counterintuitive since a zero-temperature DPRM seeks the globally minimal path through a random energy landscape. Nevertheless, the behavior is easily traced to the strong influence of the neighboring DP fixed point function. This note communicates, in part, unpublished work referenced in Phys. Rev. E58, R4096 (1998). We discovered, as well, that the RG road to asymptopia can be highly refined by bootstrapping the presumed universal distribution from the getgo...

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Timothy Halpin-Healy, Rachayl Novoseller. 2000-04-14. Tuning the trip to KPZ asymptopia. https://arxiv.org/abs/cond-mat/0004251

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