Monte Carlo calculation of the current-voltage characteristi(16)

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

experimentaldataarereproducedbytheMonteCarlosimulations.

ThereducedtemperaturevariableXusedinFig.2fortheexperimentisalsofromRef.[26]andforthelatticeCoulombgasdataweuseTc=0.218[12]determinedfroma nite

sizescalinganalysisusingEq.(6).

TheinsetinFig.2showsaselectionofexperimentaldataanalyzedalongthelines

describedinRef.[26].Thedataintheinset(plusses)arethesameasinthemain

gure,theotherdataareforBi2Sr2CaCu2Oxsinglecrystal( lledsquares)[7],andfor

Bi1.6Pb0.4Sr2Ca2Cu3Oxsinglecrystal(opensquares)[8].

TheMonteCarlodatapresentedherefora(X)areallforµ=0.0.Wealsodidthesame

analysisforMonteCarlodataforL=32andµ= 0.4, 0.2and0.2.Theclosest ttothe

experimentalresultsisproducedbyµ=0.0.Resultsfordi erentµdi erfromtheµ=0.0

results,bythatµ=0.2hasaslightlylargerderivativeatX=1andthesmallerµare

correspondinglylesssteep.

B.SelfconsistentIVcharacteristic

Inourseconddeterminationoftheexponenta(T)wewillmakeuseoftherelations

between anda(T)inequations(20-21).Theanalysisisbasedontheselfconsistent

solutionofEq.(19).Foragivencurrentdensityj,asetof (k)willbecalculatedfor

di erenttemperatures.TheselfconsistentsolutiontoEq.(19)for isshowninFig.3,

in(a)dataforT=0.18isshownandin(b)T=0.24.Thesolidanddashedstraightlines

represent =k /j2π,givenbyEq.(19),fordi erentcurrentdensitiesj.Theopencircles

represent (k )asafunctionofkfordi erentcurrentdensities.Thechoiceofthedirection

alongwhich (k )isprobedisperpendiculartothecurrentdensityj,ie.paralleltothe

vortexdriftcausedbythecurrentdensityj.Theintersectionbetweena (k )curveandthe

correspondingstraightlineisthesolutiontoEq.(19),thesearemarkedwith lledcircles.

InFig.3aforT=0.18<Tc=0.218weseethattheselfconsistentsolutiondependsonly

weaklyonthechoiceofprobingcurrentaslongasthecurrentisnottoolarge.InFig.3b