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Register a new userRKKY interaction in framework of T=0 Green function method
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A methodical derivation of RKKY interaction in framework of T=0 Green function method is given in great detail. The article is complimentary to standard textbooks on the physics of magnetism and condensed matter physics. It is shown that the methods of statistical mechanics gives a standard and probably simplest derivation of the exchange interaction. A parallel with theory of plasma waves demonstrates the relation between the Fourier transformation of polarization operator of degenerate electron gas at zero frequency and the space dependence of the indirect electron exchange due to itinerant electrons.
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We present the Stochastic Green Function (SGF) algorithm designed for bosons on lattices. This new quantum Monte Carlo algorithm is independent of the dimension of the system, works in continuous imaginary time, and is exact (no error beyond statistical errors). Hamiltonians with several species of bosons (and one-dimensional Bose-Fermi Hamiltonians) can be easily simulated. Some important features of the algorithm are that it works in the canonical ensemble and gives access to n-body Green functions.
In a recent publication (Phys. Rev E 77, 056705 (2008)),we have presented the stochastic Green function (SGF) algorithm, which has the properties of being general and easy to apply to any lattice Hamiltonian of the form H=V-T, where V is diagonal in the chosen occupation number basis and T has only positive matrix elements. We propose here a modified version of the update scheme that keeps the simplicity and generality of the original SGF algorithm, and enhances significantly its efficiency.
We theoretically clarify the functional form to be used in $t to 0$ extrapolation in the small flow time expansion (SF$t$X) method for the energy-momentum tensor (EMT), which facilitates lattice simulation of the EMT based on the gradient flow. We argue that in the $t to 0$ extrapolation analysis, lattice data should be fitted by a power function in $g(mu(t))$, the flow time dependent running coupling, where the power is determined by the perturbation order we consider. From actual lattice data, we confirm the validity of the extrapolation function. Using the new extrapolation function, we present updated lattice results for thermodynamics quantities in quenched QCD; our results are consistent with the previous study [arXiv:1812.06444] but we obtain smaller errors due to reduction of systematic errors.
We consider two fully frustrated Ising models: the antiferromagnetic triangular model in a field of strength, $h=H T k_B$, as well as the Villain model on the square lattice. After a quench from a disordered initial state to T=0 we study the nonequilibrium dynamics of both models by Monte Carlo simulations. In a finite system of linear size, $L$, we define and measure sample dependent first passage time, $t_r$, which is the number of Monte Carlo steps until the energy is relaxed to the ground-state value. The distribution of $t_r$, in particular its mean value, $< t_r(L) >$, is shown to obey the scaling relation, $< t_r(L) > sim L^2 ln(L/L_0)$, for both models. Scaling of the autocorrelation function of the antiferromagnetic triangular model is shown to involve logarithmic corrections, both at H=0 and at the field-induced Kosterlitz-Thouless transition, however the autocorrelation exponent is found to be $H$ dependent.
The determination of protein functions is one of the most challenging problems of the post-genomic era. The sequencing of entire genomes and the possibility to access genes co-expression patterns has moved the attention from the study of single proteins or small complexes to that of the entire proteome. In this context, the search for reliable methods for proteins function assignment is of uttermost importance. Previous approaches to deduce the unknown function of a class of proteins have exploited sequence similarities or clustering of co-regulated genes, phylogenetic profiles, protein-protein interactions, and protein complexes. We propose to assign functional classes to proteins from their network of physical interactions, by minimizing the number of interacting proteins with different categories. The function assignment is made on a global scale and depends on the entire connectivity pattern of the protein network. Multiple functional assignments are made possible as a consequence of the existence of multiple equivalent solutions. The method is applied to the yeast Saccharomices Cerevisiae protein-protein interaction network. Robustness is tested in presence of a high percentage of unclassified proteins and under deletion/insertion of interactions.
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