ترغب بنشر مسار تعليمي؟ اضغط هنا

Improved Lower Bounds on the Ground-State Entropy of the Antiferromagnetic Potts Model

211   0   0.0 ( 0 )
 نشر من قبل Shu-Chiuan Chang
 تاريخ النشر 2015
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

We present generalized methods for calculating lower bounds on the ground-state entropy per site, $S_0$, or equivalently, the ground-state degeneracy per site, $W=e^{S_0/k_B}$, of the antiferromagnetic Potts model. We use these methods to derive improved lower bounds on $W$ for several lattices.



قيم البحث

اقرأ أيضاً

279 - Adam Gamsa , John Cardy 2007
The scaling limit of the spin cluster boundaries of the Ising model with domain wall boundary conditions is SLE with kappa=3. We hypothesise that the three-state Potts model with appropriate boundary conditions has spin cluster boundaries which are a lso SLE in the scaling limit, but with kappa=10/3. To test this, we generate samples using the Wolff algorithm and test them against predictions of SLE: we examine the statistics of the Loewner driving function, estimate the fractal dimension and test against Schramms formula. The results are in support of our hypothesis.
213 - Yacine Ikhlef 2010
We review the exact results on the various critical regimes of the antiferromagnetic $Q$-state Potts model. We focus on the Bethe Ansatz approach for generic $Q$, and describe in each case the effective degrees of freedom appearing in the continuum limit.
We studied the non-equilibrium dynamics of the q-state Potts model in the square lattice, after a quench to sub-critical temperatures. By means of a continuous time Monte Carlo algorithm (non-conserved order parameter dynamics) we analyzed the long t erm behavior of the energy and relaxation time for a wide range of quench temperatures and system sizes. For q>4 we found the existence of different dynamical regimes, according to quench temperature range. At low (but finite) temperatures and very long times the Lifshitz-Allen-Cahn domain growth behavior is interrupted with finite probability when the system stuck in highly symmetric non-equilibrium metastable states, which induce activation in the domain growth, in agreement with early predictions of Lifshitz [JETP 42, 1354 (1962)]. Moreover, if the temperature is very low, the system always gets stuck at short times in a highly disordered metastable states with finite life time, which have been recently identified as glassy states. The finite size scaling properties of the different relaxation times involved, as well as their temperature dependency are analyzed in detail.
Fortuin-Kastelyn clusters in the critical $Q$-state Potts model are conformally invariant fractals. We obtain simulation results for the fractal dimension of the complete and external (accessible) hulls for Q=1, 2, 3, and 4, on clusters that wrap aro und a cylindrical system. We find excellent agreement between these results and theoretical predictions. We also obtain the probability distributions of the hull lengths and maximal heights of the clusters in this geometry and provide a conjecture for their form.
We calculate zeros of the $q$-state Potts model partition function on $m$th-iterate Sierpinski graphs, $S_m$, in the variable $q$ and in a temperature-like variable, $y$. We infer some asymptotic properties of the loci of zeros in the limit $m to inf ty$ and relate these to thermodynamic properties of the $q$-state Potts ferromagnet and antiferromagnet on the Sierpinski gasket fractal, $S_infty$.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا