I need an example for random electrical RC networks, where the networks are percolated for all capacitors proportions. In other words, the percolation threshold pc=0.5 means that the probability to have at least, a one resistive or capacitive percolated path is 1.
Crossover is a part of the theory of phase transitions. This part of the theory deals with the following issue. There are, say, 1st and 2nd order transitions as well as critical and tricritical points, etc. The crossover is dealing with the problem : how by changing external parameters one can smoothly go from one critical point to another or from critical point to the tricritical point-a borderline between the 1st and 2nd order transitions. This topic is fundamental for everybody who is engaged in experimental aspects of phase transitions. E.g. read this https://www.amazon.com/Elements-Transitions-Critical-Phenomena-Graduate/dp/0198754086/ref=sr_1_fkmr2_1?ie=UTF8&qid=1537818795&sr=8-1-fkmr2&keywords=avengers+phase+transitions
If you are more mathematically inclined and want to understand it from the perspective of Polymers then Karl Freed's book titled Renormalization Group theory of Macromolecules, papers of Jack Douglas, Nemirovsky from 1980's can be a good place to dive into technical aspects. Prof. Kholodenko has authored a few papers with them as well. They are the ones whole laid to foundation of crossover Phenomena in Systems with two - three body interaction terms in Edward's Hamilton. By tuning the strength of the coupling parameters corresponding to two and three body interaction term one can explore different regions of the phase diagram.
I was working with Karl Freed and I had contributed more than a half to this book. Crossover is an issue not only related to polymers and it would be good to read first references i've recommended. There are books and articles only devoted to crossover. E.g. read.
Crossover approach to global critical phenomena in fluids M.AAnisimovS.BKiselevJ.VSengersSTang
Physica A: Statistical Mechanics and its Applications
Volume 188, Issue 4, 1 October 1992, Pages 487-525 Look for papers by M.A. Anisimov and J.Sengers. They spent all their lives on this topic
Okay Arkady L. Kholodenko and Pinaki Bhattacharyya , I'll see the references which you advised me. Thank you for your responses.
Crossover phenomena simply put is different scaling laws (regime shifts in behavioral) arising by varying some control parameter. You may want to look into dielectric breakdown Phenomena using percolation model since you mentioned it in the context of resistor-capacitor networks. Google it.
Sidney Redner's these two papers may be of some use:
https://www.researchgate.net/publication/13345342_Electrical_breakdown_in_a_fuse_network_with_random_continuously_distributed_breaking_strengths
http://iopscience.iop.org/article/10.1088/0305-4470/20/13/004
Grimmet's book on percolation is a classic:
https://www.springer.com/in/book/9783540649021
Hope that helps.
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