Results 1 - 10 of 9082
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[en] We obtain lower bounds on the inverse compressibility of systems whose Lee–Yang zeros of the grand-canonical partition function lie in the left half of the complex fugacity plane. This includes in particular systems whose zeros lie on the negative real axis such as the monomer-dimer system on a lattice. We also study the virial expansion of the pressure in powers of the density for such systems. We find no direct connection between the positivity of the virial coefficients and the negativity of the L–Y zeros, and provide examples of either one or both properties holding. An explicit calculation of the partition function of the monomer-dimer system on two rows shows that there are at most a finite number of negative virial coefficients in this case. (paper)
[en] In this paper we extend previous work of Galleas and the author to elliptic SOS models. We demonstrate that the dynamical reflection algebra can be exploited to obtain a functional equation characterizing the partition function of an elliptic SOS model with domain-wall boundaries and one reflecting end. Special attention is paid to the structure of the functional equation. Through this approach we find a novel multiple-integral formula for that partition function.
[en] We study the partition function of the six-vertex model in the rational limit on arbitrary Baxter lattices with reflecting boundary. Every such lattice is interpreted as an invariant of the twisted Yangian. This identification allows us to relate the partition function of the vertex model to the Bethe wave function of an open spin chain. We obtain the partition function in terms of creation operators on a reference state from the algebraic Bethe ansatz and as a sum of permutations and reflections from the coordinate Bethe ansatz. (paper)
[en] The inequalities for spin correlation functions of ferromagnetic Ising models with pair interactions derived in a previous paper are studied in more detail. It is shown that each of these inequalities is a positive linear combination of a finite number of 'extremal' inequalities, which can in principle be determined and of which a number of examples is given. (orig.)
[de]Die in einer frueheren Abhandlung abgeleiteten Ungleichungen fuer Spin-Korrelations-Funktionen von ferromagnetischen Ising-Modellen mit Paar-Wechselwirkungen werden genauer untersucht. Es wird gezeigt, dass jede dieser Ungleichungen eine positive Linearkombination einer endlichen Anzahl von 'extremalen' Ungleichungen ist, die im Prinzip bestimmt werden kann und von denen eine Reihe von Beispielen gegeben wird. (orig.)
[en] In this work, we consider an upper bound for the quantum mutual information in thermal states of a bipartite quantum system. This bound is related with the interaction energy and logarithm of the partition function of the system. We demonstrate the connection between this upper bound and the value of the mutual information for the bipartite system realized by two spin-1/2 particles in the external magnetic field with the XY-Heisenberg interaction
[en] We show how to represent a class of expressions involving discrete sums over partitions as matrix models. We apply this technique to the partition functions of 2* theories, i.e. Seiberg-Witten theories with the massive hypermultiplet in the adjoint representation. We consider theories in four, five, and six dimensions, and obtain new matrix models, respectively, of rational, trigonometric, and elliptic type. The matrix models for five- and six-dimensional U(1) theories are derived from the topological vertex construction related to curves of genus one and two.
[en] We compute the grand partition function of N=4 SYM at one-loop in the SU(2) sector with general chemical potentials, extending the results of Pólya’s theorem. We make use of finite group theory, applicable to all orders of perturbative 1/Nc expansion. We show that only the planar terms contribute to the grand partition function, which is therefore equal to the grand partition function of an ensemble of XXX(1/2) spin chains. We discuss how Hagedorn temperature changes on the complex plane of chemical potentials.
[en] AGT conjecture connects Nekrasov instanton partition function of 4D quiver gauge theory with 2D Liouville conformal blocks. We re-investigate this connection using the central extension of spherical Hecke algebra in q-coordinate representation, q being the instanton expansion parameter. Based on AFLT basis together with intertwiners we construct gauge conformal state and demonstrate its equivalence to the Liouville conformal state, with careful attention to the proper scaling behavior of the state. Using the colliding limit of regular states, we obtain the formal expression of irregular conformal states corresponding to Argyres–Douglas theory, which involves summation of functions over Young diagrams.
[en] Instantaneous quantum polynomial-time (IQP) computation is a class of quantum computation consisting only of commuting two-qubit gates and is not universal. Nevertheless, it has been shown that if there is a classical algorithm that can simulate IQP efficiently, the polynomial hierarchy collapses to the third level, which is highly implausible. However, the origin of the classical intractability is still less understood. Here we establish a relationship between IQP and computational complexity of calculating the imaginary-valued partition functions of Ising models. We apply the established relationship in two opposite directions. One direction is to find subclasses of IQP that are classically efficiently simulatable by using exact solvability of certain types of Ising models. Another direction is applying quantum computational complexity of IQP to investigate (im)possibility of efficient classical approximations of Ising partition functions with imaginary coupling constants. Specifically, we show that a multiplicative approximation of Ising partition functions is #P-hard for almost all imaginary coupling constants even on planar lattices of a bounded degree. (paper)
[en] The structure of topological theory coupled to topological gravity is studied. We show that in this theory Q-exact terms do not decouple. This not decoupling in the action of the theory is connected with the existence of boundaries of the moduli space and leads to problems in defining the topological gravity for massive topological theories. Not decoupling of Q-exact observables leads to filtration of the gravitational descendants constructed from matter fields. Two a priori different preferred splittings of this filtration are constructed (one connected with the massive deformation of the theory and the other connected with the flatness of the connection on the space of theories). It is conjectured that they coincide