Browsing by Author "Geyer, H. B."
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- ItemNonperturbative flow equations from running expectation values(American Physical Society (APS), 2003-08) Scholtz, F. G.; Bartlett, Bruce H.; Geyer, H. B.We show that Wegner’s flow equations, as recently discussed in the Lipkin model, can be solved selfconsistently. This leads to a nonlinear differential equation which fully determines the order parameter as a function of the dimensionless coupling constant, even across the phase transition. Since we consider an expansion in the fluctuations, rather than the conventional expansion in the coupling constant, convergence to the exact results is found in both phases when taking the thermodynamic limit.
- ItemOn the thermodynamic limit at a quantum critical point(Academy of Science for South Africa, 2005) Geyer, H. B.; Heiss, W. D.; Scholtz, F. G.Open questions regarding the uniqueness and existence of the thermodynamic limit at a quantum critical point are discussed in the context of the Lipkin model, a popular model in many-body theory. This model illustrates a quantum phase transition, including spontaneous symmetry breaking. The thermodynamic limit seemingly yields different answers depending on the approach used. The discussion is based on recent developments, including a joint publication by the authors.