Monte Carlo calculation of the current-voltage characteristi(14)

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

jumpcriteriontellsusthat1/ (k=0)jumpsfrom4TcatT=Tc to0atT=Tc+[9].Apracticaldi cultyforlocatingTcfromMonteCarlodataonsmalllatticeswiththis

procedureisthatextrapolationtothek=0limitrequireslargelattices,asthesmallest

nonzerokis2π/L.Thecorrespondingquantityto1/ (k=0)inthetwodimensionalXY

modeliscalledthehelicitymodulusγ[5].Bothquantitieshavebeenusedtolocatethe

Kosterlitz-ThoulesstransitiontemperatureinMonteCarlocalculations[5,25,19].

InthedataanalysisinthenextsectionweuseanalternativeproceduretolocateTcfrom

thelinearresistance[12].WeobtainthelinearresistanceRfromtheNyquistformulain

Eq.(5)forasequenceofsystemsizesLandtemperaturesT.AccordingtoEq.(6)data

forL2Rfordi erentsystemsizesshouldbecomesystemsizeindependentatthecritical

temperature,whichisourcriteriontolocateTc.Thiscircumventsthedi cultiesofusing

1/ (k=0).ThetwodeterminationsgivewithinerrorbarsthesamevalueforTc.

V.RESULTS

WepresentMonteCarlosimulationresultsforthreedi erentdeterminationsoftheIV

exponenta(T)forthe2DCoulombgasmodel.Theresultsweshowhereareforthechemical

potentialµ=0.0andlatticesizeL=32ifnotdi erentlystated.

A.NonlinearIVexponent

Our rstmethodconsistsinadirectmeasurementoftheelectric eldEinducedbyan

appliedcurrentdensityj.InFig.1aresultsfortheIVcharacteristicofthetwo-dimensional

Coulombgasareshown.Thedashedlineintheln(E)versusln(j)plothasslopethree

andrepresentstheslopeatT=Tcaccordingtotheuniversaljumpcondition[9].The

solidcurvesrepresentresultsfordi erenttemperatures.Forveryhighcurrentthevoltage

responsesaturates.Thisisbecausewhenallattemptstomovethevorticesinthedirection

oftheLorentzforcearealreadyaccepted,furtherincreasingthecurrentcannotgivemore

voltage.Forlowenoughcurrentthereisacrossovertoohmicresistance,whenthecurrent