The effect of lattice vibration on the second-order phase transition for the Ising model is investigated. The total Hamiltonian of the system is separated into the phonon part and the spin part, if the displacement of the atoms from their equilibrium position is assumed to be small. The spin part of the free energy is then calculated (i) in the molecular-field approximation for the square and the simple cubic lattices, and (ii) by the method due to Kadanoff, a modification of the Onsager's exact solution, for the square lattice. The results show that (i) the phase transition remains to be of the second order, (ii) the critical temperature increases, and (iii) the magnetic part of the heat capacity decreases, both for ferro- and antiferromagnetic Ising models.The effect of lattice vibration on the second-order phase transition for the Ising model is investigated. The total Hamiltonian of the system is separated into the phonon part and the spin part, if the displacement of the atoms from their equilibrium position is assumed to be small. The spin part of the free energy is then calculated (i) in the molecular-field approximation for the square and the simple cubic lattices, and (ii) by the method due to Kadanoff, a modification of the Onsager's exact solution, for the square lattice. The results show that (i) the phase transition remains to be of the second order, (ii) the critical temperature increases, and (iii) the magnetic part of the heat capacity decreases, both for ferro- and antiferromagnetic Ising models.

Journal of the Physical Society of JapanNov 1, 196830 citations

Systems with separable many-particle interactions. II

L.W.J. den Ouden, Hans W. Capel, Jacques H. H. Perk

Physica A Statistical Mechanics and its ApplicationsJan 1, 197641 citations

Space-Time Method forAb InitioCalculations of Self-Energies and Dielectric Response Functions of Solids

H. Rojas, Rex W. Godby, Richard J. Needs

We present a new method for efficient, accurate calculations of many-body properties of periodic systems. The main features are (i) use of a real-space/imaginary-time representation, (ii) avoidance of any model form for the screened interaction $W$ , (iii) exact separation of $W$ and the self-energy $\ensuremath{\Sigma}$ into short- and long-ranged parts, and (iv) the use of novel analytical continuation techniques in the energy domain. The computer time scales approximately linearly with system size. We give results for jellium and silicon, including the spectral function of silicon obtained from the Dyson equation.We present a new method for efficient, accurate calculations of many-body properties of periodic systems. The main features are (i) use of a real-space/imaginary-time representation, (ii) avoidance of any model form for the screened interaction $W$, (iii) exact separation of $W$ and the self-energy $\ensuremath{\Sigma}$ into short- and long-ranged parts, and (iv) the use of novel analytical continuation techniques in the energy domain. The computer time scales approximately linearly with system size. We give results for jellium and silicon, including the spectral function of silicon obtained from the Dyson equation.

Physical Review LettersMar 6, 1995266 citations

All transformations of coordinates that separate the center of mass kinetic energy, their group structure and geometry

L. Fortunato

The most general transformations of coordinates that allow for the exact separation of the kinetic energy operator of a quantum many-body system into total center of mass kinetic energy and internal kinetic energy are found and discussed. It is found (i) that the suitable transformations, depending on the number of particles, have a certain number of free parameters and this allows for the generalization of the Jacobi coordinates to a much larger class of coordinates with the same properties and (ii) that there is a new, uncommon, additive group structure hidden in the transformation matrices that is connected to certain geometric properties of the set of coordinates.The most general transformations of coordinates that allow for the exact separation of the kinetic energy operator of a quantum many-body system into total center of mass kinetic energy and internal kinetic energy are found and discussed. It is found (i) that the suitable transformations, depending on the number of particles, have a certain number of free parameters and this allows for the generalization of the Jacobi coordinates to a much larger class of coordinates with the same properties and (ii) that there is a new, uncommon, additive group structure hidden in the transformation matrices that is connected to certain geometric properties of the set of coordinates.

arXiv:0910.2811Journal of Physics A Mathematical and TheoreticalJan 19, 20102 citations

W

, (iii) exact separation of

W

and the self-energy $\ensuremath{\Sigma}$ into short- and long-ranged parts, and (iv) the use of novel analytical continuation techniques in the energy domain. The computer time scales approximately linearly with system size. We give results for jellium and silicon, including the spectral function of silicon obtained from the Dyson equation.