Monte Carlo calculation of the current-voltage characteristi(3)

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

assumestheuniversalvalue2,soV～I3atT=Tc.ForT<Tconehasa(T)>2,andfor

T>Tconehasa(T)=0(forsmallenoughcurrents)[9].Experimentson,forexample,thinHg-Xealloy lms[4]andalsoforcertainsinglecrystalhightemperaturesuperconductors

[7,8],amongsome,havecon rmedthis.

SinceIVcharacteristicsarehardtocalculateanalyticallycomputersimulationisauseful

tool.IVcharacteristicsofvortexsystemshaverecentlybeencalculatedsuccessfullywith

MonteCarlosimulations[10].LinearandnonlinearIVcharacteristicsofvortexglasssuper-

conductorshavebeenreportedinRefs.[10,11].InarecentMonteCarlosimulationofthe

CoulombgasthelinearresistancewasusedtolocatetheKosterlitz-Thoulesstransition[12].

ThenonlinearIVcharacteristicsattheKosterlitz-Thoulesstransitionhasbeencalculated

inRef.[13],anda nite-sizescalinganalysisaccuratelyveri edtherelationV～I3atthe

Kosterlitz-Thoulesstransition.

InthispaperwestudytheIVcharacteristicsofalatticeCoulombgasmodelbyMonte

Carlosimulationsofvortexdynamics.WecalculatetheIVexponenta(T)oftheCoulomb

gasinthreedi erentways:(1)BydirectMonteCarlocalculationofthenonlinearresistance,

(2)byaselfconsistentlinearscreeningconstructionfortheenergybarrierforcurrentin-

ducedvortex-pairbreakinggivingthermallyactivatedresistance,and(3)bya nitescaling

constructionfromdataforthelinearresistance.AllmethodsarebasedonMonteCarlo

simulations,andweapplybothequilibriumandnon-equilibriumsimulations.Thesethree

methodsgivethesameresults,givingusaconsistentandsimplepictureofnonequilibrium

responseinthissystem.Furthermore,wecompareourresultsfora(T)withexperiments.

Scalingargumentsgivethata(T)isauniversalscalingfunctionofareducedCoulombgas

temperatureX=T/Tc,andthisisveri edinexperiments[3].We ndcloseagreement

betweenourMonteCarloresultsandtheexperimentaluniversalscalingcurve,andthis

comparisonappearstobepresentedhereforthe rsttime.Theagreementbetweendif-

ferentmethods,andbetweenoursimulationsandexperiments,arethemainresultsofour

paper.SomeofourMonteCarloresultsforthenonlinearIVcharacteristicshavebeen

obtainedpreviously[13],asexplainedabove.