Improved lower bounds on the ground-state entropy of the antiferromagnetic Potts model.
نویسندگان
چکیده
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.
منابع مشابه
Upper and Lower Bounds for Ground State Entropy of Antiferromagnetic Potts Models
We derive rigorous upper and lower bounds for the ground state entropy of the q-state Potts antiferromagnet on the honeycomb and triangular lattices. These bounds are quite restrictive, especially for large q. ∗email: [email protected] ∗∗email: [email protected] Nonzero ground state disorder and associated entropy, S0 6= 0, is an important subject in statistical mechan...
متن کاملLower bounds on the ground-state entropy of the Potts antiferromagnet on slabs of the simple cubic lattice.
We calculate rigorous lower bounds for the ground-state degeneracy per site, W, of the q-state Potts antiferromagnet on slabs of the simple cubic lattice that are infinite in two directions and finite in the third and that thus interpolate between the square (sq) and simple cubic (sc) lattices. We give a comparison with large-q series expansions for the sq and sc lattices and also present numer...
متن کاملExact valence bond entanglement entropy and probability distribution in the XXX spin chain and the potts model.
We determine exactly the probability distribution of the number N_(c) of valence bonds connecting a subsystem of length L>>1 to the rest of the system in the ground state of the XXX antiferromagnetic spin chain. This provides, in particular, the asymptotic behavior of the valence-bond entanglement entropy S_(VB)=N_(c)ln2=4ln2/pi(2)lnL disproving a recent conjecture that this should be related w...
متن کاملAntiferromagnet on the Honeycomb Lattice
We study the q-state Potts antiferromagnet with q = 3 on the honeycomb lattice. Using an analytic argument together with a Monte Carlo simulation, we conclude that this model is disordered for all T ≥ 0. We also calculate the ground state entropy to be S0/kB = 0.507(10) and discuss this result. ∗email: [email protected] ∗∗email: [email protected] The effect of ground s...
متن کاملThe ferro / antiferromagnetic q - state Potts model
The critical properties of the mixed ferro/antiferromagnetic q-state Potts model on the square lattice are investigated using the numerical transfer matrix technique. The transition temperature is found to be substantially lower than previously found for q = 3. It is conjectured that there is no transition for q > 3, in contradiction with previous results.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Physical review. E, Statistical, nonlinear, and soft matter physics
دوره 91 5 شماره
صفحات -
تاریخ انتشار 2015