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Monte Carlo methods were used to calculate heat capacities as functions oftemperature for classical atomic clusters of aggregate sizes $25 \leq N \leq60$ that were bound by pairwise Lennard-Jones potentials. The paralleltempering method was used to overcome convergence difficulties due toquasiergodicity in the solid-liquid phase-change regions. All of the clustersstudied had pronounced peaks in their heat capacity curves, most of whichcorresponded to their solid-liquid phase-change regions. The heat capacity peakheight and location exhibited two general trends as functions of cluster size:for $N = 25$ to 36, the peak temperature slowly increased, while the peakheight slowly decreased, disappearing by $N = 37$; for $N = 30$, a very smallsecondary peak at very low temperature emerged and quickly increased in sizeand temperature as $N$ increased, becoming the dominant peak by $N = 36$.Superimposed on these general trends were smaller fluctuations in the peakheights that corresponded to ``magic number'' behavior, with local maxima foundat $N = 36, 39, 43, 46$ and 49, and the largest peak found at $N = 55$. Thesemagic numbers were a subset of the magic numbers found for other clusterproperties, and can be largely understood in terms of the clusters' underlyinggeometries. Further insights into the melting behavior of these clusters wereobtained from quench studies and by examining rms bond length fluctuations.Comment: 15 pages, 17 figures (PDF format

Magic number behavior for heat capacities of medium-sized classical Lennard-Jones clusters