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Cavity Method
The cavity method is a mathematical method presented by Marc Mézard, Giorgio Parisi and Miguel Angel Virasoro in 1987 to solve some mean field type models in statistical physics, specially adapted to disordered systems. The method has been used to compute properties of ground states in many condensed matter and optimization problems. Initially invented to deal with the Sherrington–Kirkpatrick model of spin glasses, the cavity method has shown wider applicability. It can be regarded as a generalization of the Bethe— Peierls iterative method in tree-like graphs, to the case of a graph with loops that are not too short. The different approximations that can be done with the cavity method are usually named after their equivalent with the different steps of the replica method which is mathematically more subtle and less intuitive than the cavity approach. The cavity method has proved useful in the solution of optimization problems such as k-satisfiability and graph coloring. It ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marc Mézard
Marc Mézard (born 29 August 1957) is a French physicist and academic administrator. He was, from 2012 to 2022, the director of the ''École normale supérieure'' (ENS). He is the co-author of two books. Early life Marc Mézard was born on 29 August 1957. He graduated from the ''École normale supérieure'' in 1976 and earned the '' agrégation'' in Physics. He earned a PhD in Physics from University of Paris 6 in 1980. Career Mézard joined the ''Centre national de la recherche scientifique'' (CNRS) as a researcher in 1981. He was a professor of Physics at the ''École Polytechnique''. In 2001, he joined the Center for Theoretical Physics and Statistical Models at the University of Paris-Sud, and he serves as its director. Since 2012 to 2022, he had also served as the director of his alma mater, the ENS. In 2022 he joined the Department of the Computing Sciences at the Bocconi University in Milan. Mézard is the author of 170 academic articles and the co-author of two books. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Giorgio Parisi
Giorgio Parisi (born 4 August 1948) is an Italian theoretical physicist, whose research has focused on quantum field theory, statistical mechanics and complex systems. His best known contributions are the QCD evolution equations for parton densities, obtained with Guido Altarelli, known as the Altarelli–Parisi or DGLAP equations, the exact solution of the Sherrington–Kirkpatrick model of spin glasses, the Kardar–Parisi–Zhang equation describing dynamic scaling of growing interfaces, and the study of whirling flocks of birds. He was awarded the 2021 Nobel Prize in Physics jointly with Klaus Hasselmann and Syukuro Manabe for groundbreaking contributions to theory of complex systems, in particular "for the discovery of the interplay of disorder and fluctuations in physical systems from atomic to planetary scales." Career Giorgio Parisi received his degree from the University of Rome La Sapienza in 1970 under the supervision of Nicola Cabibbo. He was a researcher a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Miguel Ángel Virasoro (physicist)
Miguel Ángel Virasoro (; Buenos Aires, 9 May 1940 – Buenos Aires, 23 July 2021) was an Argentine ( naturalized Italian) theoretical physicist. Virasoro worked in Argentina, Israel, the United States, and France, but he spent most of his professional career in Italy at La Sapienza University of Rome. He shared a name with his father, the philosopher Miguel Ángel Virasoro. He was known for his foundational work in string theory, the study of spin glasses, and his research in other areas of mathematical and statistical physics. The Virasoro-Shapiro amplitude,Virasoro, M. (1969). "Alternative constructions of crossing-symmetric amplitudes with Regge behavior." ''Physical Review'', 177(5), 2309–2311. the Virasoro algebra, the super Virasoro algebra, the Virasoro vertex operator algebra, the Virasoro group, the Virasoro conjecture, the Virasoro conformal block, and the Virasoro minimal model are all named after him. Biography Early life in Argentina Miguel Ángel Virasoro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mean Field
In physics and probability theory, Mean-field theory (MFT) or Self-consistent field theory studies the behavior of high-dimensional random (stochastic) models by studying a simpler model that approximates the original by averaging over degrees of freedom (the number of values in the final calculation of a statistic that are free to vary). Such models consider many individual components that interact with each other. The main idea of MFT is to replace all interactions to any one body with an average or effective interaction, sometimes called a ''molecular field''. This reduces any many-body problem into an effective one-body problem. The ease of solving MFT problems means that some insight into the behavior of the system can be obtained at a lower computational cost. MFT has since been applied to a wide range of fields outside of physics, including statistical inference, graphical models, neuroscience, artificial intelligence, epidemic models, queueing theory, computer-network ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Physics
Statistical physics is a branch of physics that evolved from a foundation of statistical mechanics, which uses methods of probability theory and statistics, and particularly the mathematical tools for dealing with large populations and approximations, in solving physical problems. It can describe a wide variety of fields with an inherently stochastic nature. Its applications include many problems in the fields of physics, biology, chemistry, and neuroscience. Its main purpose is to clarify the properties of matter in aggregate, in terms of physical laws governing atomic motion. Statistical mechanics develop the phenomenological results of thermodynamics from a probabilistic examination of the underlying microscopic systems. Historically, one of the first topics in physics where statistical methods were applied was the field of classical mechanics, which is concerned with the motion of particles or objects when subjected to a force. Scope Statistical physics explains and quanti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ground State
The ground state of a quantum-mechanical system is its stationary state of lowest energy; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state. In quantum field theory, the ground state is usually called the vacuum state or the vacuum. If more than one ground state exists, they are said to be degenerate. Many systems have degenerate ground states. Degeneracy occurs whenever there exists a unitary operator that acts non-trivially on a ground state and commutes with the Hamiltonian of the system. According to the third law of thermodynamics, a system at absolute zero temperature exists in its ground state; thus, its entropy is determined by the degeneracy of the ground state. Many systems, such as a perfect crystal lattice, have a unique ground state and therefore have zero entropy at absolute zero. It is also possible for the highest excited state to have absolute zero te ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Condensed Matter
Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid phases which arise from electromagnetic forces between atoms. More generally, the subject deals with "condensed" phases of matter: systems of many constituents with strong interactions between them. More exotic condensed phases include the superconducting phase exhibited by certain materials at low temperature, the ferromagnetic and antiferromagnetic phases of spins on crystal lattices of atoms, and the Bose–Einstein condensate found in ultracold atomic systems. Condensed matter physicists seek to understand the behavior of these phases by experiments to measure various material properties, and by applying the physical laws of quantum mechanics, electromagnetism, statistical mechanics, and other theories to develop mathematical models. The diversity of systems and phenomena available for study makes condensed matter ph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optimization Problem
In mathematics, computer science and economics, an optimization problem is the problem of finding the ''best'' solution from all feasible solutions. Optimization problems can be divided into two categories, depending on whether the variables are continuous or discrete: * An optimization problem with discrete variables is known as a '' discrete optimization'', in which an object such as an integer, permutation or graph must be found from a countable set. * A problem with continuous variables is known as a ''continuous optimization'', in which an optimal value from a continuous function must be found. They can include constrained problems and multimodal problems. Continuous optimization problem The '' standard form'' of a continuous optimization problem is \begin &\underset& & f(x) \\ &\operatorname & &g_i(x) \leq 0, \quad i = 1,\dots,m \\ &&&h_j(x) = 0, \quad j = 1, \dots,p \end where * is the objective function to be minimized over the -variable vector , * are called ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sherrington–Kirkpatrick Model
In condensed matter physics, a spin glass is a magnetic state characterized by randomness, besides cooperative behavior in freezing of spins at a temperature called 'freezing temperature' ''Tf''. In ferromagnetic solids, component atoms' magnetic spins all align in the same direction. Spin glass when contrasted with a ferromagnet is defined as " disordered" magnetic state in which spins are aligned randomly or without a regular pattern and the couplings too are random. The term "glass" comes from an analogy between the ''magnetic'' disorder in a spin glass and the ''positional'' disorder of a conventional, chemical glass, e.g., a window glass. In window glass or any amorphous solid the atomic bond structure is highly irregular; in contrast, a crystal has a uniform pattern of atomic bonds. In ferromagnetic solids, magnetic spins all align in the same direction; this is analogous to a crystal's lattice-based structure. The individual atomic bonds in a spin glass are a m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spin Glass
In condensed matter physics, a spin glass is a magnetic state characterized by randomness, besides cooperative behavior in freezing of spins at a temperature called 'freezing temperature' ''Tf''. In ferromagnetic solids, component atoms' magnetic spins all align in the same direction. Spin glass when contrasted with a ferromagnet is defined as " disordered" magnetic state in which spins are aligned randomly or without a regular pattern and the couplings too are random. The term "glass" comes from an analogy between the ''magnetic'' disorder in a spin glass and the ''positional'' disorder of a conventional, chemical glass, e.g., a window glass. In window glass or any amorphous solid the atomic bond structure is highly irregular; in contrast, a crystal has a uniform pattern of atomic bonds. In ferromagnetic solids, magnetic spins all align in the same direction; this is analogous to a crystal's lattice-based structure. The individual atomic bonds in a spin glass are a mixt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hans Bethe
Hans Albrecht Bethe (; July 2, 1906 – March 6, 2005) was a German-American theoretical physicist who made major contributions to nuclear physics, astrophysics, quantum electrodynamics, and solid-state physics, and who won the 1967 Nobel Prize in Physics for his work on the theory of stellar nucleosynthesis. For most of his career, Bethe was a professor at Cornell University.Available at www.JamesKeckCollectedWorks.or are the class notes taken by one of his students at Cornell from the graduate courses on Nuclear Physics and on Applications of Quantum Mechanics he taught in the spring of 1947. During World War II, he was head of the Theoretical Division at the secret Los Alamos National Laboratory, Los Alamos laboratory that developed the first atomic bombs. There he played a key role in calculating the critical mass of the weapons and developing the theory behind the implosion method used in both the Trinity test and the "Fat Man" weapon dropped on Nagasaki in August ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rudolf Peierls
Sir Rudolf Ernst Peierls, (; ; 5 June 1907 – 19 September 1995) was a German-born British physicist who played a major role in Tube Alloys, Britain's nuclear weapon programme, as well as the subsequent Manhattan Project, the combined Allied nuclear bomb programme. His obituary in ''Physics Today'' described him as "a major player in the drama of the eruption of nuclear physics into world affairs". Peierls studied physics at the University of Berlin, at the University of Munich under Arnold Sommerfeld, the University of Leipzig under Werner Heisenberg, and ETH Zurich under Wolfgang Pauli. After receiving his DPhil from Leipzig in 1929, he became an assistant to Pauli in Zurich. In 1932, he was awarded a Rockefeller Fellowship, which he used to study in Rome under Enrico Fermi, and then at the Cavendish Laboratory at the University of Cambridge under Ralph H. Fowler. Because of his Jewish background, he elected to not return home after Adolf Hitler's rise to power in 19 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
