Monte Carlo calculation of the current-voltage characteristi(18)

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

as

TheobtainedscalingexponentaRasafunctionoftemperatureisshowninFig.7.AsacomparisonwealsoshowdataforaIV(T)fromFig.2,obtainedfromdirectevaluation

oftheIVcharacteristic.The nitesizescalinganalysisinFig.6breaksdownforlow

temperatures.ThiscanbeseenbythedeviationofaR(T)fromthedataforaIV(T)at

T=0.15.InFig.7thisdeviationisalsoevident.Acarefulinspectionofthescalingat

temperaturesT=0.15andT=0.18revealsthattheorderofthelatticessizesisreversed

forT=0.15comparedwiththehighertemperatures.Thismayberelatedtothedi culties

toconvergethesimulationatlowtemperature. aL,L′(R(L)L R(L′)L′a)2.TheconsideredlatticesizesareL,L′=6,8,12,16,24,32.

VI.DISCUSSION

WehavecalculatedthenonlinearIVexponentaIV(T)ofthetwodimensionallattice

Coulombgas.Ourresultsarebasedonthreedi erentdeterminations.Adirectcalculation

parisonwithexperiments

[4,7,8,26]onHg-Xe lmsandsinglecrystalhighTcsuperconductorsshowgoodagreement.

Oursecondmethodisbasedonasimpleselfconsistentcalculationofthedielectric

function attheunbindingseparation,andtheIVexponentcanthenbecalculated.Here

weespeciallyfocusonthecomparisonoftworelationsbetweena(T)and .The rstrelation

Eq.(20)[17]isbasedonordinarydi usionintwodimensionswitharecombinationrate

proportionalton2F.Thesecondexpressionfora(T)giveninEq.(21)hasbeenderivedfrom

ascalinganalysis[21].

We ndthattheexponentdeterminedbyEq.(21)fortemperaturesbelowTcisclose

tothemoredirectdeterminedaIV(T)andwillthereforealso ttheexperimentsforthese

temperatures.

ThethirdmethodisbasedonequilibriumMonteCarlosimulations.Fromthescaling

relationEq.(17)forthelinearresistancewecanderiveaR(T).We ndthatthescaling

exponentaR(T)toahighdegreeofaccuracy tsthedirectdeterminedaIV(T)forabroad