Numerically we simulate the short-time behaviour of the critical dynamics for the two dimensional Ising model and Potts model with an initial state of very high temperature and small magnetization. Critical initial increase of the magnetization is observed. The new dynamic critical exponent θ as well as the exponents z and 2β/ν are determined from the power law behaviour of the magnetization, auto-correlation and the second moment. Furthermore the calculation has been carried out with both Heat-bath and Metropolis algorithms. All the results are consistent and therefore universality and scaling are confirmed.
Dynamic relaxation of the XY model quenched from a high temperature state to the critical temperature or below is investigated with Monte Carlo methods. When a non-zero initial magnetization is given, in the short-time regime of the dynamic evolution the critical initial increase of the magnetization is observed. The dynamic exponent θ is directly determined. The results show that the exponent θ varies with respect to the temperature. Furthermore, it is demonstrated that this initial increase of the magnetization is universal, i.e. independent of the microscopic details of the initial configurations and the algorithms.
In the numerical simulation of certain field theoretical models, the complex Langevin simulation has been believed to fail due to the violation of ergodicity. We give a detailed analysis of this problem based on a toy model with one degree of freedom (S = −β cos θ). We find that the failure is not due to the defect of complex Langevin simulation itself, but rather to the way how one treats the singularity appearing in the drift force. An effective algorithm is proposed by which one can simulate the 1/β behaviour of the expectation value < cos θ > in the small β limit.
The angular distrubutions for dileptons arising from decays of a virtual photon and the Z 0 produced in hadronic collisions are calculated at large mass and finite transverse momentum of dileptons in the lowest order of quantum chromodynamics and the Weinberg-Salam model with threee fermion generations. Numerical evaluation for coefficients of the distributions is carried out for pp collisions at 6 =540 GeV and pp at ds =800 GeV in different (helicity, Gottfried-Jackson, and Collins-Soper) reference frames. Coefficients of parity-violating terms in the distributions exhibit clean signs of the Z 0 boson, while those of parity-conserving terms are quite insensitive to the presence of the Z 0 boson.
Among various models proposed so far, attempting to explain the anomalous I + l -y events, four representative types of models, (I) ZO-s or P + y -l + l -y , (11) z~-z~, , , + -l + l -y (anomalous-magnetic-moment interaction), (111) zO-TI* + I T * + l + l P y (excited lepton), and (IV) S or P-z:,, + y , are confronted with a test of the distribution in the angle between photon and one of the leptons. All these four models seem to fail to provide the explanation to the angular characteristics of the data. However, more statistics are needed to arrive at firm conclusions with regards to the mechanism of the events, including as well the bremsstrahlung contribution.
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