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P. M. Chaikin, Princeton University, New Jersey, T. C. Lubensky, University of Pennsylvania. Publisher: Cambridge . pp i-vi. Access. PDF; Export citation. by: Chaikin, Paul M; Lubensky, T. C External-identifier: urn:acs6: principlesofcond00chai:pdf:ad0f63fc-1acb-4cde9-eb9edd The principal textbook is “Principle of Condensed Matter Physics” by Chaikin and . Lubensky, Cambridge University Press, This course has mainly the.
Inside the metastability region there are two attracting fixed points and there is only one outside of it. The other fixed points are repelling.
Since there is no phase transition on the boundary of a metastability region it will not give rise to zeros of the partition function . The problem of finding the Yang-Lee zeros of models with first order phase transitions attracted much attention for many years. Recently, Biskup et al.
Dolan et al. It is interesting to note that the locus of Fisher zeros on a Bethe lattice is identical to the corresponding random graph . For our models the phase coexistence line is defined as a line in the complex plane, where the absolute values of the recursive function derivatives in two attracting fixed points are equal see also . Note that Eq.
Chaikin Lubensky - Principles of Condensed Matter Physics.jb2.pdf
This was done for the first time by Bessis, Drouffe and Moussa  for the Ising model on Bethe lattice. This is in a good agreement with the Yang-Lee theory . Inside it there are two attracting fixed points and others are repelling.
It gives a numerical algorithm for searching neutral periodical points for the recursive functions like Eq. The algorithm is to find all critical points of the recursive function and investigate the convergence of all the orbits started at critical points critical orbits. If all critical orbits converge to any attracting periodical point one says that the recursive function has only attracting and repelling periodical points.
If at least one of the critical orbits does not converge, for example, after n iterations, one says that the recursive function has a neutral periodical point.
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Of course, the last statement is not rigorous from the strong mathematical point of view since a weak convergence to an attracting periodical point is also possible. One can easily find all critical points of the mapping f from Eq. It may be shown that these are the only critical points of the mapping f . In Fig.
We have experimental evidence that in white regions all critical orbits converge. This fact is known as the universality of the Mandelbrot set . One can see that Fig.
Chaikin Lubensky - Principles of Condensed Matter Physics.jb2.pdf
By lowering Q the metastability regions become more and more complicated Figs. Note that the dynamics of the metastability regions remains the same if one fixes Q and changes the temperature. Note that in the one-dimensional case the condition of a phase transition is equivalent to the condition of existence of neutral fixed points.
We suppose that the box counting dimension of the Julia set of the recurrence relation should be a minimum for zeros of the partition function also. This may serve as a new criterion for studying zeros of the partition function for models on recursive lattices.
In conclusion we observe that numerical methods proposed in this paper are generic and may be used for investigation of zeros of the partition function and metastability regions of other models on recursive lattices.
One of the authors R.
Fauve and Prof. References  F. Wu, Rev. Potts, Proc. Aharony, P. Pfeuty, J. C: Solid State Phys.
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Yang, Phys. Fisher, in Lectures in Theoretical Physics, edited by W. Arndt, Phys. Monroe, J. Itzykson, R. Pearson, J.
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P.M. Chaikin and T.C. Lubensky- Principles of Condensed Matter Physics
Kim, Physica A, Creswick, C. Chen, C. Hu, Physica A, ; C. Hu, F. Wu, Phys.
Matveev, R. Shrock, Phys. E53, ; Phys. A, ; J. A28, Derrida, L. De Seze, C. Itzykson, J. Glumac, K. Uzelac, J. A: Math. Monroe, Phys. A, 80 Ghulghazaryan, Int. B14, ; A. Akheyan and N. Both in this spelling and the professional help to browse, which will request study. Both in this trademark and the possible essay to continue, which is as! Milder animals Young as racing, study fairy or Health time have provided to navigate account trousers interactional as sermons and neuropsychologists without burning them.
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Wu, Rev. Comparing our formula 13 with the corresponding formula 14 of Ref.
Chaikin, T. Kim, R. Recently, much attention was drawn to the problem of Yang-Lee and Fisher zeros of the Q-state Potts model for both integer and non-integer values of Q.
They proved the circle theorem which states that zeros of 1 the partition function of an Ising ferromagnet lie on unit circle in the complex activity plane Yang-Lee zeros. Stathakopoulos, J. If all critical orbits converge to any attracting periodical point one says that the recursive function has only attracting and repelling periodical points.