Markov Chain Monte Carlo simulation data for the preprint. T010ad***S10000M*_1.txt: simulation history for a_{dig} = 0.3, 0.5, 0.7, m^2 = 1, -1, B_max = 5000, used for Table 1 and Figure 1. T010R100L401S10000M1_1.txt: simulation history for a_{dig} = 0.5, m^2 = 1, B_max = 1, used for Figure 2. Table2.zip: contains simulation history for Table 2 and Figure 3. File name "T1a0.2S1250M1L4s2101.txt" indicates that the temperature is 1, a_{dig} = 0.2, Delta = 1250, m^2 = 1, lattice size is 4 * 4, and the random seed is 2101. Lines contain the expectation values of the potential energy and the two correlation functions obtained for successive steps. The largest estimated auto-correlation length d_q, which is used for the analysis, is as follows: adig d(0,0) d(π,π) 0.2 37 4 0.25 38 4 0.3 37 4 0.4 41 4 0.5 59 5 0.6 130 7 0.7 369 15 0.8 968 55 0.9 2174 148 1.0 4491 319 The initial 10 d_q steps are discarded as a burn-in period, regardless of whether we conducted a warm-up run prior to the steps contained in this dataset.