遵守莫训
Undecidability of Critical Lattice Constants under Turing CompletenessDefinitions & Notation1. Lattice Space: Let mathcal{L} = mathbb{Z}^2 be a two-dimensional square lattice with lattice constant a. Define local spin variables sigma_i in {-1, +1} and the Hamiltonian: H({sigma}; a) = -J(a) sum_{langle i,j rangle} sigma_i sigma_j - h sum_i sigma_i where the exchange integral J(a) is a smooth function of a satisfying J'(a) delta^? If so, derive the analytical relationship between delta^ and the critical exponent beta.3. Meta-mathematical Reflection (Bonus): Does the above result imply that, in real physical systems, the operation of "precisely measuring the lattice constant to the phase transition critical point" is computationally equivalent to solving an NP-complete problem? Provide a formal argument based on the Church-Turing-Deutsch principle.
发布于 河北
分享
评论
赞
未登录
友善发言
评论
加载中
