On the Kertész line: Some rigorous bounds

Details On the Kertész line: Some rigorous bounds On the Kertész line: Some rigorous bounds

2008-02-13

arxiv.org/abs/0802.1826v1

Journal of Mathematical Physics 49 (2008) 053303

Physics

Condensed Matter

Statistical Mechanics

11 pages, 1 figure

Scientific paper

10.1063/1.2924322

We study the Kert\'esz line of the $q$--state Potts model at (inverse) temperature $\beta$, in presence of an external magnetic field $h$. This line separates two regions of the phase diagram according to the existence or not of an infinite cluster in the Fortuin-Kasteleyn representation of the model. It is known that the Kert\'esz line $h_K (\beta)$ coincides with the line of first order phase transition for small fields when $q$ is large enough. Here we prove that the first order phase transition implies a jump in the density of the infinite cluster, hence the Kert\'esz line remains below the line of first order phase transition. We also analyze the region of large fields and prove, using techniques of stochastic comparisons, that $h_K (\beta)$ equals $\log (q - 1) - \log (\beta - \beta_p)$ to the leading order, as $\beta$ goes to $\beta_p = - \log (1 - p_c)$ where $p_c$ is the threshold for bond percolation.

Affiliated with

Also associated with

No associations

Rating

On the Kertész line: Some rigorous bounds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the Kertész line: Some rigorous bounds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Kertész line: Some rigorous bounds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-676750