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High Precision Measurement Of The Thermal Exponent For The Three-Dimensional Xy Universality Class, Evgeni Burovski, Jonathan Machta, Nikolay Prokof'ev, Boris Svitunov
High Precision Measurement Of The Thermal Exponent For The Three-Dimensional Xy Universality Class, Evgeni Burovski, Jonathan Machta, Nikolay Prokof'ev, Boris Svitunov
Jonathan Machta
Simulation results are reported for the critical point of the two-component ϕ4 field theory. The correlation-length exponent is measured to high precision with the result ν=0.6717(3). This value is in agreement with recent simulation results [Campostrini et al., Phys. Rev. B 63, 214503 (2001)] and marginally agrees with the most recent space-based measurements of the superfluid transition in He4 [Lipa et al., Phys. Rev. B 68, 174518 (2003)].
Complexity, Parallel Computation And Statistical Physics, Jonathan Machta
Complexity, Parallel Computation And Statistical Physics, Jonathan Machta
Jonathan Machta
The intuition that a long history is required for the emergence of complexity in natural systems is formalized using the notion of depth. The depth of a system is defined in terms of the number of parallel computational steps needed to simulate it. Depth provides an objective, irreducible measure of history that is applicable to systems of the kind studied in statistical physics. It is argued that physical complexity cannot occur in the absence of substantial depth and that depth is a useful proxy for physical complexity. The ideas are illustrated for a variety of systems in statistical physics
Numerical Study Of The Random Field Ising Model At Zero And Positive Temperature, Yong Wu, Jonathan Machta
Numerical Study Of The Random Field Ising Model At Zero And Positive Temperature, Yong Wu, Jonathan Machta
Jonathan Machta
In this paper the three-dimensional random-field Ising model is studied at both zero temperature and positive temperature. Critical exponents are extracted at zero temperature by finite size scaling analysis of large discontinuities in the bond energy. The heat capacity exponent α is found to be near zero. The ground states are determined for a range of external field and disorder strength near the zero temperature critical point and the scaling of ground state tilings of the field-disorder plane is discussed. At positive temperature the specific heat and the susceptibility are obtained using the Wang-Landau algorithm. It is found that sharp …