Abstract
Melting of systems of hard disks by Monte Carlo simulations
Highlights
Despite the enormous effort spent studying twodimensional melting over a time span of several decades, the nature of this phase transition remains a matter of controversy
Our main conclusions follow: ͑1͒ the melting transition is of second order; ͑2͒ ͗͘ drops discontinuouslyfrom͘ϭ0.74Ϯ0.02) to zero at the melting point; and3͒ we find no hexatic phaseif it exists for systems of hard disks, the range for it is within about 1% of the melting volume value. ͓S1063-651X97͒10201-X
The vertical line is at the melting point value, vmϭ1.261
Summary
Despite the enormous effort spent studying twodimensional melting over a time span of several decades, the nature of this phase transition remains a matter of controversy. We can obtain reliable equilibrium values for volume fluctuations(␦v)2͘ for systems of many thousands of particles only because equilibration times are not as forbiddingly long for HCW’s as they are for PBC’s. ͓ P() is approximately size independent for 64рNр1024, once again in accordance with a second order phase transition.͔ Yet further evidence that supports the conclusion that͘ vanishes discontinuously upon melting, as predicted by Nelson and Halperin, is provided in Sec. IV: a plot of(␦͉͉)2͘ versus͘, for systems of different sizes. Each run was divided into five intervals; the standard deviation of the five corresponding values of the quantity of interest is given as its error
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