article
Formation of stripes and slabs near the ferromagnetic transition
published
yes
Alessandro
Giuliani
author
Élliott
Lieb
author
Robert
Seiringer
author 4AFD0470-F248-11E8-B48F-1D18A9856A87
RoSe
department
We consider Ising models in d = 2 and d = 3 dimensions with nearest neighbor ferromagnetic and long-range antiferromagnetic interactions, the latter decaying as (distance)-p, p > 2d, at large distances. If the strength J of the ferromagnetic interaction is larger than a critical value J c, then the ground state is homogeneous. It has been conjectured that when J is smaller than but close to J c, the ground state is periodic and striped, with stripes of constant width h = h(J), and h → ∞ as J → Jc -. (In d = 3 stripes mean slabs, not columns.) Here we rigorously prove that, if we normalize the energy in such a way that the energy of the homogeneous state is zero, then the ratio e 0(J)/e S(J) tends to 1 as J → Jc -, with e S(J) being the energy per site of the optimal periodic striped/slabbed state and e 0(J) the actual ground state energy per site of the system. Our proof comes with explicit bounds on the difference e 0(J)-e S(J) at small but positive J c-J, and also shows that in this parameter range the ground state is striped/slabbed in a certain sense: namely, if one looks at a randomly chosen window, of suitable size ℓ (very large compared to the optimal stripe size h(J)), one finds a striped/slabbed state with high probability.
Springer2014
eng
Communications in Mathematical Physics10.1007/s00220-014-1923-2
3311333 - 350
A. Giuliani, É. Lieb, and R. Seiringer, “Formation of stripes and slabs near the ferromagnetic transition,” <i>Communications in Mathematical Physics</i>, vol. 331, no. 1, pp. 333–350, 2014.
Giuliani A, Lieb É, Seiringer R. Formation of stripes and slabs near the ferromagnetic transition. <i>Communications in Mathematical Physics</i>. 2014;331(1):333-350. doi:<a href="https://doi.org/10.1007/s00220-014-1923-2">10.1007/s00220-014-1923-2</a>
Giuliani A, Lieb É, Seiringer R. 2014. Formation of stripes and slabs near the ferromagnetic transition. Communications in Mathematical Physics. 331(1), 333–350.
Giuliani, A., Lieb, É., & Seiringer, R. (2014). Formation of stripes and slabs near the ferromagnetic transition. <i>Communications in Mathematical Physics</i>, <i>331</i>(1), 333–350. <a href="https://doi.org/10.1007/s00220-014-1923-2">https://doi.org/10.1007/s00220-014-1923-2</a>
Giuliani, Alessandro, et al. “Formation of Stripes and Slabs near the Ferromagnetic Transition.” <i>Communications in Mathematical Physics</i>, vol. 331, no. 1, Springer, 2014, pp. 333–50, doi:<a href="https://doi.org/10.1007/s00220-014-1923-2">10.1007/s00220-014-1923-2</a>.
Giuliani, Alessandro, Élliott Lieb, and Robert Seiringer. “Formation of Stripes and Slabs near the Ferromagnetic Transition.” <i>Communications in Mathematical Physics</i> 331, no. 1 (2014): 333–50. <a href="https://doi.org/10.1007/s00220-014-1923-2">https://doi.org/10.1007/s00220-014-1923-2</a>.
A. Giuliani, É. Lieb, R. Seiringer, Communications in Mathematical Physics 331 (2014) 333–350.
19352018-12-11T11:54:48Z2019-08-02T12:37:31Z