We develop an optimized perturbation theory for the Ginzburg Landau description of thermal fluctu... more We develop an optimized perturbation theory for the Ginzburg Landau description of thermal fluctuations effects in the vortex liquids. Unlike the high temperature expansion which is asymptotic, the optimized expansion is convergent. Radius of convergence on the lowest Landau level is aT = −3 in 2D and aT = −5 in 3D. It allows a systematic calculation of magnetization and specific heat contributions due to thermal fluctuations of vortices in strongly type II superconductors to a very high precision. The results are in good agreement with existing Monte Carlo simulations and experiments. Limitations of various nonperturbative and phenomenological approaches are noted. In particular we show that there is no exact intersection point of the magnetization curves both in 2D and 3D. PACS numbers: 74.60.-w, 74.40.+k, 74.25.Ha, 74.25.Dw ∗e-mail: lidp@phys.nthu.edu.tw †e-mail: baruch@vortex1.ep.nctu.edu.tw
We developed a systematic non-perturbative method base on Dyson-Schwinger theory and the derivabl... more We developed a systematic non-perturbative method base on Dyson-Schwinger theory and the derivable theory for Ising model at broken phase. Based on these methods, we obtain critical temperature and spin spin correlation beyond mean field theory. The spectrum of Green function obtained from our methods become gapless at critical point, so the susceptibility become divergent at Tc. The critical temperature of Ising model obtained from this method is fairly good in comparison with other non-cluster methods. It is straightforward to extend this method to more complicate spin models for example with continue symmetry.
A systematic calculation of magnetization and specific heat contributions due to fluctuations of ... more A systematic calculation of magnetization and specific heat contributions due to fluctuations of vortex lattice in strongly type II superconductors to precision of 1% is presented. We complete the calculation of the two loop low temperature perturbation theory by including the umklapp processes. Then the gaussian variational method is adapted to calculation of thermodynamic characteristics of the 2D and the 3D vortex solids in high magnetic field. Based on it as a starting point for a perturbation theory we calculate the leading correction providing simultaneously an estimate of precision. The results are compared to existing nonperturbative approaches. PACS numbers: 74.60.-w, 74.40.+k, 74.25.Ha, 74.25.Dw ∗e-mail: lidp@mono1.math.nctu.edu.tw †e-mail: baruch@vortex1.ep.nctu.edu.tw
Ginzburg–Landau theory is an important tool in condensed matter physics research, describing the ... more Ginzburg–Landau theory is an important tool in condensed matter physics research, describing the ordered phases of condensed matter, including the dynamics, elasticity, and thermodynamics of the condensed configurations. In this systematic introduction to Ginzberg–Landau theory, both common and topological excitations are considered on the same footing (including their thermodynamics and dynamical phenomena). The role of the topological versus energetic considerations is made clear. Required mathematics (symmetry, including lattice translation, topology, and perturbative techniques) are introduced as needed. The results are illustrated using arguably the most fascinating class of such systems, high Tc superconductors subject to magnetic field. This book is an important reference for both researchers and graduate students working in condensed matter physics or can act as a textbook for those taking advanced courses on these topics.
We develop an optimized perturbation theory for the Ginzburg Landau description of thermal fluctu... more We develop an optimized perturbation theory for the Ginzburg Landau description of thermal fluctuations effects in the vortex liquids. Unlike the high temperature expansion which is asymptotic, the optimized expansion is convergent. Radius of convergence on the lowest Landau level is aT = −3 in 2D and aT = −5 in 3D. It allows a systematic calculation of magnetization and specific heat contributions due to thermal fluctuations of vortices in strongly type II superconductors to a very high precision. The results are in good agreement with existing Monte Carlo simulations and experiments. Limitations of various nonperturbative and phenomenological approaches are noted. In particular we show that there is no exact intersection point of the magnetization curves both in 2D and 3D. PACS numbers: 74.60.-w, 74.40.+k, 74.25.Ha, 74.25.Dw ∗e-mail: lidp@phys.nthu.edu.tw †e-mail: baruch@vortex1.ep.nctu.edu.tw
We developed a systematic non-perturbative method base on Dyson-Schwinger theory and the derivabl... more We developed a systematic non-perturbative method base on Dyson-Schwinger theory and the derivable theory for Ising model at broken phase. Based on these methods, we obtain critical temperature and spin spin correlation beyond mean field theory. The spectrum of Green function obtained from our methods become gapless at critical point, so the susceptibility become divergent at Tc. The critical temperature of Ising model obtained from this method is fairly good in comparison with other non-cluster methods. It is straightforward to extend this method to more complicate spin models for example with continue symmetry.
A systematic calculation of magnetization and specific heat contributions due to fluctuations of ... more A systematic calculation of magnetization and specific heat contributions due to fluctuations of vortex lattice in strongly type II superconductors to precision of 1% is presented. We complete the calculation of the two loop low temperature perturbation theory by including the umklapp processes. Then the gaussian variational method is adapted to calculation of thermodynamic characteristics of the 2D and the 3D vortex solids in high magnetic field. Based on it as a starting point for a perturbation theory we calculate the leading correction providing simultaneously an estimate of precision. The results are compared to existing nonperturbative approaches. PACS numbers: 74.60.-w, 74.40.+k, 74.25.Ha, 74.25.Dw ∗e-mail: lidp@mono1.math.nctu.edu.tw †e-mail: baruch@vortex1.ep.nctu.edu.tw
Ginzburg–Landau theory is an important tool in condensed matter physics research, describing the ... more Ginzburg–Landau theory is an important tool in condensed matter physics research, describing the ordered phases of condensed matter, including the dynamics, elasticity, and thermodynamics of the condensed configurations. In this systematic introduction to Ginzberg–Landau theory, both common and topological excitations are considered on the same footing (including their thermodynamics and dynamical phenomena). The role of the topological versus energetic considerations is made clear. Required mathematics (symmetry, including lattice translation, topology, and perturbative techniques) are introduced as needed. The results are illustrated using arguably the most fascinating class of such systems, high Tc superconductors subject to magnetic field. This book is an important reference for both researchers and graduate students working in condensed matter physics or can act as a textbook for those taking advanced courses on these topics.
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