Phase transitions for random colourings
نویسنده
چکیده
The results concerning long range order for random colourings on planar quasi-transitive graphs will be explained and the proof will be outlined. Based on joint works with A. Sokal and J. Swart.
منابع مشابه
Magnetic Properties and Phase Transitions in a Spin-1 Random Transverse Ising Model on Simple Cubic Lattice
Within the effective-field theory with correlations (EFT), a transverse random field spin-1 Ising model on the simple cubic (z=6) lattice is studied. The phase diagrams, the behavior of critical points, transverse magnetization, internal energy, magnetic specific heat are obtained numerically and discussed for different values of p the concentration of the random transverse field.
متن کاملRandom Colourings and Automorphism Breaking in Locally Finite Graphs
A colouring of a graph G is called distinguishing if its stabiliser in AutG is trivial. It has been conjectured that, if every automorphism of a locally finite graph moves infinitely many vertices, then there is a distinguishing 2-colouring. We study properties of random 2-colourings of locally finite graphs and show that the stabiliser of such a colouring is almost surely nowhere dense in AutG...
متن کاملPlanting Colourings Silently
Let k ≥ 3 be a fixed integer and let Zk(G) be the number of k-colourings of the graph G. For certain values of the average degree, the random variable Zk(G(n,m)) is known to be concentrated in the sense that 1 n (lnZk(G(n,m)) − lnE[Zk(G(n,m))]) converges to 0 in probability [Achlioptas and Coja-Oghlan: Proc. FOCS 2008]. In the present paper we prove a significantly stronger concentration result...
متن کاملSampling colourings of the triangular lattice
We show that the Glauber dynamics on proper 9-colourings of the triangular lattice is rapidly mixing, which allows for efficient sampling. Consequently, there is a fully polynomial randomised approximation scheme (FPRAS) for counting proper 9-colourings of the triangular lattice. Proper colourings correspond to configurations in the zero-temperature anti-ferromagnetic Potts model. We show that ...
متن کاملReconstruction of Random Colourings
Reconstruction problems have been studied in a number of contexts including biology, information theory and and statistical physics. We consider the reconstruction problem for random k-colourings on the ∆-ary tree for large k. Bhatnagar et. al. [1] showed non-reconstruction when ∆ ≤ 1 2 k log k − o(k log k) and reconstruction when ∆ ≥ k log k + o(k log k). We tighten this result and show nonrec...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013