Monte Carlo calculation of the current-voltage characteristi(7)

We have studied the nonlinear current-voltage characteristic of a two dimensional lattice Coulomb gas by Monte Carlo simulation. We present three different determinations of the power-law exponent $a(T)$ of the nonlinear current-voltage characteristic, $V

B.Thermallyactivatedresistance

Theabovescalingargumentledtoa nitesizescalingformulawhichisusefulforlocating

thetransitiontemperaturefromMonteCarlodatafortheresistanceof nitesamples.Here

wewilldoamoredetailedanalysisthatwillalsoleadtothesameformula.Theanalysishere

doesnotdirectlyinvolvescalingarguments,butconsiderstheinteractionsbetweenvortices

intheCoulombgas.Theanalysiswillgiveexpressionsfortheresistancefromthermally

activatedfreevorticesintheCoulombgasinthepresenceofanappliedsupercurrent.This

moredetailedanalysiswillbeusefulinlatersectionswhenweanalyzeMonteCarlodatafor

theCoulombgas.

AccordingtotheJosephsonrelationthevoltageVcausedbyvortexmotionis

V～d φ

I～nF(7)

Tomakeanestimateofthedensityoffreevorticesweproceedbythefollowingsimplemodel.

TheenergyE(r)ofavortexpairofseparationr>r0inthepresenceofacurrentIis[17]:

E(r)=E0+E1ln(r

2π

(k)