% spising2D   Hamiltonian for the 2D Ising model with aperiodic boundary condition; sparse%            version.%   spising2D(B,Nx,Ny) gives the Hamiltonian as a sparse matrix for the %   ferromagnetic Ising model in transverse field for Nx*Ny qubits, if the %   field strength is B and the coefficient %   of the nearest neighbor coupling is 1. %   That is, the Hamiltonian is H= - sum_k z(k) z(k+1) + B*sum_k x(k), %   where x and z denote Pauli spin matrices.%   The coupling is z-z and the direction of the field is x. %   For the Hamiltonian aperiodic boundary condition is used.% Copyright (C) 2006  Geza Toth    E.mail: toth@alumni.nd.edu%% This program is free software; you can redistribute it and/or% modify it under the terms of the GNU General Public License% as published by the Free Software Foundation; see gpl.txt% of this subroutine package.%% This program is distributed in the hope that it will be useful,% but WITHOUT ANY WARRANTY; without even the implied warranty of% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the% GNU General Public License for more details.% % You should have received a copy of the GNU General Public License% along with this program; if not, write to the Free Software% Foundation, Inc., 51 Franklin Street, Fifth Floor, % Boston, MA  02110-1301, USA.function H=spising2D(BField,Nx,Ny)x=[0 1;1 0];y=[0 -i;i 0]; z=[1 0; 0 -1];e=[1 0; 0 1];% Using routines from the library to make the Ising HamiltonianH=-splattice(z,z,Nx,Ny)+BField*spcoll(x,Nx*Ny);