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estimate of the infinite volume K,. With this and re-weighted data generated from it in hand we use the appropriate finite size scaling relations to derive estimates of the critical exponents and temperature. Estimate of v: This is obtained from the finite size scaling of the maxima of thermodynamic derivatives of U, log |m|, and log m? [6]. For example, d(logm?)/dK = (m?E)/(m?) — (E) is calculated as a function of K using the histogram H(E,m) to re-weight the data. FSS analysis to extract v is done keeping only the

Figure 3 estimate of the infinite volume K,. With this and re-weighted data generated from it in hand we use the appropriate finite size scaling relations to derive estimates of the critical exponents and temperature. Estimate of v: This is obtained from the finite size scaling of the maxima of thermodynamic derivatives of U, log |m|, and log m? [6]. For example, d(logm?)/dK = (m?E)/(m?) — (E) is calculated as a function of K using the histogram H(E,m) to re-weight the data. FSS analysis to extract v is done keeping only the

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‘ig. 2: Estimates of \; as a function of the blocking level n for simulations at different couplings kK. The best estimate of the extrapolated value with w = 0.85 is from the fit to the diamonds skipping n = 0,1 points. The fit to all the diamond points is, for comparison, shown by the dotted line.
‘ig. 2: Estimates of \; as a function of the blocking level n for simulations at different couplings kK. The best estimate of the extrapolated value with w = 0.85 is from the fit to the diamonds skipping n = 0,1 points. The fit to all the diamond points is, for comparison, shown by the dotted line.
The values obtained from the derivative of log|m| and logm? agree, while that from U is higher by its 1c error estimate. These estimates are higher than the MCRG value by roughly one combined c. as we cannot reliably include correction terms with data at only 3 values of Z. Linear fits to the maximum value versus L1/” are shown in Fig. 4. The quality of the fits is exceedingly good, and the final results are where the values of a’ and b’ are different for each thermodynamic quantity. The three data points for each quantity shown in Fig. 5 have been joined together by straight lines to highlight the deviations from linearity. With just three lattice sizes we cannot include the correction term (2.e. w), to take into account the
The values obtained from the derivative of log|m| and logm? agree, while that from U is higher by its 1c error estimate. These estimates are higher than the MCRG value by roughly one combined c. as we cannot reliably include correction terms with data at only 3 values of Z. Linear fits to the maximum value versus L1/” are shown in Fig. 4. The quality of the fits is exceedingly good, and the final results are where the values of a’ and b’ are different for each thermodynamic quantity. The three data points for each quantity shown in Fig. 5 have been joined together by straight lines to highlight the deviations from linearity. With just three lattice sizes we cannot include the correction term (2.e. w), to take into account the
Table 4. FSS estimates of K¢,, from different observables as a function of v. where the first error is statistical and the second is an estimate of the systematic error based on the variation with observable type. This value is lower than that obtained by Ferrenberg and Landau (6], but consistent with our MCRG result.
Table 4. FSS estimates of K¢,, from different observables as a function of v. where the first error is statistical and the second is an estimate of the systematic error based on the variation with observable type. This value is lower than that obtained by Ferrenberg and Landau (6], but consistent with our MCRG result.
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