Solving the Schrödinger equation for the Sherrington - Kirkpatrick model in a transverse field
نویسندگان
چکیده
منابع مشابه
Solving the Schrödinger equation for the Sherrington–Kirkpatrick model in a transverse field
By numerically solving the Schrödinger equation for small sizes we investigate the quantum critical point of the infinite-range Ising spin glass in a transverse field at zero temperature. Despite its simplicity the method yields accurate information on the value of the critical field and critical exponents. We obtain 0c = 1.47± 0.01 and check that exponents are in agreement with analytical appr...
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The Sherrington-Kirkpatrick (SK) model was introduced by David Sherrington and Scott Kirkpatrick in 1975 as a simple ‘solvable’ (in their words) model for spin-glasses. Spin-glasses are some type of magnetic alloys, and ‘solvable’ meant that the asymptotic free entropy density could be computed exactly. It turns out that the original SK solution was incorrect and in fact inconsistent (the autho...
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The state of art in spin glass field theory is reviewed. We start from an Edwards-Anderson-type model in finite dimensions, with finite but long range forces, construct the effective field theory that allows one to extract the long wavelength behaviour of the model, and set up an expansion scheme (the loop expansion) in the inverse range of the interaction. At the zeroth order we recover mean f...
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In [10] Michel Talagrand gave a rigorous proof of the Parisi formula in the SherringtonKirkpatrick model. In this paper we build upon the methodology developed in [10] and extend Talagrand’s result to a more general class of mean field models with spins distributed according to an arbitrary probability measure on the bounded subset of the real line and with external field term given by an arbit...
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برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 1997
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/30/4/001