Relevant bibliographies by topics / Exact partition function

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Academic literature on the topic 'Exact partition function'

Author: Grafiati
Published: 14 March 2023

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Journal articles on the topic "Exact partition function"

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PUTROV, PAVEL, and MASAHITO YAMAZAKI. "EXACT ABJM PARTITION FUNCTION FROM TBA." Modern Physics Letters A 27, no. 34 (November 2, 2012): 1250200. http://dx.doi.org/10.1142/s0217732312502008.

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We report on the exact computation of the S3 partition function of U (N)k × U (N)-k ABJM theory for k = 1, N = 1, …, 19. The result is a polynomial in π-1 with rational coefficients. As an application of our results, we numerically determine the coefficient of the membrane 1-instanton correction to the partition function.
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Hatsuda, Yasuyuki, Sanefumi Moriyama, and Kazumi Okuyama. "Exact instanton expansion of the ABJM partition function." Progress of Theoretical and Experimental Physics 2015, no. 11 (October 28, 2015): 11B104. http://dx.doi.org/10.1093/ptep/ptv145.

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Izmailov, Alexander F., and Alexander R. Kessel. "Exact quantum partition function of the BCS model." International Journal of Theoretical Physics 29, no. 10 (October 1990): 1073–90. http://dx.doi.org/10.1007/bf00672086.

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Bouttier, J., P. Di Francesco, and E. Guitter. "Random trees between two walls: exact partition function." Journal of Physics A: Mathematical and General 36, no. 50 (December 1, 2003): 12349–66. http://dx.doi.org/10.1088/0305-4470/36/50/001.

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HATZINIKITAS, AGAPITOS, and IOANNIS SMYRNAKIS. "CLOSED BOSONIC STRING PARTITION FUNCTION IN TIME INDEPENDENT EXACT pp-WAVE BACKGROUND." International Journal of Modern Physics A 21, no. 05 (February 20, 2006): 995–1013. http://dx.doi.org/10.1142/s0217751x06025493.

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The modular invariance of the one-loop partition function of the closed bosonic string in four dimensions in the presence of certain homogeneous exact pp -wave backgrounds is studied. In the absence of an axion field, the partition function is found to be modular invariant and equal to the free field partition function. The partition function remains unchanged also in the presence of a fixed axion field. However, in this case, the covariant form of the action suggests summation over all possible twists generated by the axion field. This is shown to modify the partition function. In the light-cone gauge, the axion field generates twists only in the worldsheet σ-direction, so the resulting partition function is not modular invariant, hence wrong. To obtain the correct partition function one needs to sum over twists in the t-direction as well, as suggested by the covariant form of the action away from the light-cone gauge.
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Julian Lee. "Exact Partition Function Zeros of Two-Dimensional Lattice Polymers." Journal of the Korean Physical Society 44, no. 3 (March 15, 2004): 617. http://dx.doi.org/10.3938/jkps.44.617.

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Basu-Mallick, B., and Nilanjan Bondyopadhaya. "Exact partition function of supersymmetric Haldane–Shastry spin chain." Nuclear Physics B 757, no. 3 (November 2006): 280–302. http://dx.doi.org/10.1016/j.nuclphysb.2006.09.009.

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Zhang, Degang. "Exact Solution for Three-Dimensional Ising Model." Symmetry 13, no. 10 (October 1, 2021): 1837. http://dx.doi.org/10.3390/sym13101837.

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The three-dimensional Ising model in a zero external field is exactly solved by operator algebras, similar to the Onsager’s approach in two dimensions. The partition function of the simple cubic crystal imposed by the periodic boundary condition along two directions and the screw boundary condition along the third direction is calculated rigorously. In the thermodynamic limit an integral replaces a sum in the formula of the partition function. The critical temperatures, at which order–disorder transitions in the infinite crystal occur along three axis directions, are determined. The analytical expressions for the internal energy and the specific heat are also presented.
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González, Gabriel. "Exact Partition Function for the Random Walk of an Electrostatic Field." Advances in Mathematical Physics 2017 (2017): 1–5. http://dx.doi.org/10.1155/2017/6970870.

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The partition function for the random walk of an electrostatic field produced by several static parallel infinite charged planes in which the charge distribution could be either ±σ is obtained. We find the electrostatic energy of the system and show that it can be analyzed through generalized Dyck paths. The relation between the electrostatic field and generalized Dyck paths allows us to sum overall possible electrostatic field configurations and is used for obtaining the partition function of the system. We illustrate our results with one example.
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Kogan, Yaakov. "Exact analysis for a class of simple, circuit-switched networks with blocking." Advances in Applied Probability 21, no. 4 (December 1989): 952–55. http://dx.doi.org/10.2307/1427782.

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We consider the same circuit switching problem as in Mitra [1]. The calculation of the blocking probabilities is reduced to finding the partition function for a closed exponential pseudo-network with L−1 customers. This pseudo-network differs from that in [1] in one respect only: service rates at nodes 1, 2, …, p depend on the queue length. The asymptotic expansion developed in [1] follows from our exact expression for the partition function.
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Books on the topic "Exact partition function"

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Guhr, Thomas. Replica approach in random matrix theory. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.8.

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This article examines the replica method in random matrix theory (RMT), with particular emphasis on recently discovered integrability of zero-dimensional replica field theories. It first provides an overview of both fermionic and bosonic versions of the replica limit, along with its trickery, before discussing early heuristic treatments of zero-dimensional replica field theories, with the goal of advocating an exact approach to replicas. The latter is presented in two elaborations: by viewing the β = 2 replica partition function as the Toda lattice and by embedding the replica partition function into a more general theory of τ functions. The density of eigenvalues in the Gaussian Unitary Ensemble (GUE) and the saddle point approach to replica field theories are also considered. The article concludes by describing an integrable theory of replicas that offers an alternative way of treating replica partition functions.
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Henriksen, Niels Engholm, and Flemming Yssing Hansen. Bimolecular Reactions, Transition-State Theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805014.003.0006.

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This chapter discusses an approximate approach—transition-state theory—to the calculation of rate constants for bimolecular reactions. A reaction coordinate is identified from a normal-mode coordinate analysis of the activated complex, that is, the supermolecule on the saddle-point of the potential energy surface. Motion along this coordinate is treated by classical mechanics and recrossings of the saddle point from the product to the reactant side are neglected, leading to the result of conventional transition-state theory expressed in terms of relevant partition functions. Various alternative derivations are presented. Corrections that incorporate quantum mechanical tunnelling along the reaction coordinate are described. Tunnelling through an Eckart barrier is discussed and the approximate Wigner tunnelling correction factor is derived in the limit of a small degree of tunnelling. It concludes with applications of transition-state theory to, for example, the F + H2 reaction, and comparisons with results based on quasi-classical mechanics as well as exact quantum mechanics.
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Book chapters on the topic "Exact partition function"

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Wilson, Robin. "9. Partitions." In Combinatorics: A Very Short Introduction, 140–50. Oxford University Press, 2016. http://dx.doi.org/10.1093/actrade/9780198723493.003.0009.

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How many ways can a number be split into two, three, or more pieces? ‘Partitions’ considers this interesting problem and the way in which Leonard Euler started to investigate them around 1740. Euler considered the generating function of the sequence of partition numbers and devised his pentagonal number formula. His publication Introduction to the Analysis of Infinities in 1748 outlined the difference between distinct and odd partitions. Many mathematicians worked on the partition problem, but it was not resolved until G. H. Hardy and his collaborator Srinivasa Ramanujan in 1918 published an exact formula for partition numbers using a new method in the theory of numbers called the ‘circle method’.
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Mussardo, Giuseppe. "Minimal Conformal Models." In Statistical Field Theory, 399–442. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198788102.003.0011.

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Chapter 11 discusses the so-called minimal conformal models, all of which are characterized by a finite number of representations. It goes on to demonstrate how all correlation functions of these models satisfy linear differential equations. It shows how their explicit solutions are given by using the Coulomb gas method. It also explains how their exact partition functions can be obtained by enforcing the modular invariance of the theory. The chapter also covers null vectors, the Kac determinant, unitary representations, operator product expansion, fusion rules, Verlinde algebra, screening operators, structure constants, the Landau–Ginzburg formulation, modular invariance, and Torus geometry. The appendix covers hypergeometric functions.
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Conference papers on the topic "Exact partition function"

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Agrawal, Durgesh, Yash Pote, and Kuldeep S. Meel. "Partition Function Estimation: A Quantitative Study." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. California: International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/587.

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Probabilistic graphical models have emerged as a powerful modeling tool for several real-world scenarios where one needs to reason under uncertainty. A graphical model's partition function is a central quantity of interest, and its computation is key to several probabilistic reasoning tasks. Given the #P-hardness of computing the partition function, several techniques have been proposed over the years with varying guarantees on the quality of estimates and their runtime behavior. This paper seeks to present a survey of 18 techniques and a rigorous empirical study of their behavior across an extensive set of benchmarks. Our empirical study draws up a surprising observation: exact techniques are as efficient as the approximate ones, and therefore, we conclude with an optimistic view of opportunities for the design of approximate techniques with enhanced scalability. Motivated by the observation of an order of magnitude difference between the Virtual Best Solver and the best performing tool, we envision an exciting line of research focused on the development of portfolio solvers.
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Giovannelli, J. F. "Estimation of the Ising field parameter thanks to the exact partition function." In 2010 17th IEEE International Conference on Image Processing (ICIP 2010). IEEE, 2010. http://dx.doi.org/10.1109/icip.2010.5650185.

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Deshpande, Moreshwar, and C. D. Mote. "Intermodal Coupling in Flexible Spinning Disk-Spindle Systems." In ASME 1999 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/detc99/vib-8143.

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Abstract The coupling between the disk and spindle vibration modes of a rotating disk-spindle system is analyzed through the free vibrations of a rotating, flexible spindle with N attached flexible disks. The spindle is modeled as an extensible Kirchhoff-Love rod and the disks as Kirchhoff plates. Couplings between the longitudinal, torsional and flexural deformations of the spindle and the transverse and in-plane motions of the disk are studied analytically. A kinematically rich model captures couplings that have not been predicted previously. Discretization of these modes as a series of orthonormal functions allows for the construction of the characteristic matrix. The structure of this matrix is exploited to partition the eigenvalue problem into six natural classes and to provide simple, exact rules governing the coupling between the modes of the disk-spindle system. The longitudinal spindle vibration modes and the zero nodal diameter transverse disk modes are coupled inertially at all rotation speeds. The torsional spindle modes couple to the zero nodal diameter in-plane disk modes at all non-zero rotation speeds. This coupling is absent in a stationary disk-spindle system. For non-zero rotation speeds, the flexural modes of the spindle in the two orthogonal planes containing the undeformed spindle centerline and the one nodal diameter transverse and in-plane disk modes couple. The one nodal diameter transverse disk modes couple to the one nodal diameter in-plane disk modes through the flexural compliance of the spindle; this coupling cannot be observed through study of the disk alone.
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