By Igor Herbut

ISBN-10: 0511249403

ISBN-13: 9780511249402

ISBN-10: 0521854520

ISBN-13: 9780521854528

Severe phenomena is without doubt one of the most enjoyable parts of contemporary physics. This 2007 ebook presents a radical yet financial advent into the rules and methods of the speculation of serious phenomena and the renormalization crew, from the point of view of recent condensed subject physics. Assuming simple wisdom of quantum and statistical mechanics, the e-book discusses section transitions in magnets, superfluids, superconductors, and gauge box theories. specific consciousness is given to subject matters similar to gauge box fluctuations in superconductors, the Kosterlitz-Thouless transition, duality variations, and quantum part transitions - all of that are on the vanguard of physics study. This publication comprises various difficulties of various levels of hassle, with suggestions. those difficulties supply readers with a wealth of fabric to check their figuring out of the topic. it really is excellent for graduate scholars and more matured researchers within the fields of condensed subject physics, statistical physics, and many-body physics.

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**Extra resources for A Modern Approach to Critical Phenomena **

**Example text**

To summarize, we have introduced six critical exponents to describe singular behavior of various thermodynamic functions and of the correlation function near the magnetic and liquid–gas critical points. We introduced the scaling ansatz for the free energy and the correlation function, and derived four equations (including hyperscaling) for the exponents, reducing the number of independent exponents to only two. Whenever the hyperscaling holds, we may then compute the correlation length exponent ν and the anomalous dimension η, for example, to determine all six critical exponents.

We will see that in contrast to the remaining three scaling laws the hyperscaling is not always satisfied. To summarize, we have introduced six critical exponents to describe singular behavior of various thermodynamic functions and of the correlation function near the magnetic and liquid–gas critical points. We introduced the scaling ansatz for the free energy and the correlation function, and derived four equations (including hyperscaling) for the exponents, reducing the number of independent exponents to only two.

4* Consider the quantum phase transition at T = 0 in the theory with the action β S= dτ dr |∂τ (r , τ )|2 + |∇ (r , τ )|2 − μ| (r , τ )|2 0 + λ | (r , τ )|4 , N where is the N -component complex field, like in the previous problem. Find the critical exponents in general dimension when N → ∞. 3 but with d replaced by d + 1. There is no transition for d ≤ 1, and the critical exponents have the mean-field values for d > 3. 5 Upper critical dimension Landau’s mean-field theory, at least in the normal phase, may be understood as the zeroth order approximation in the interaction strength λ.

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