Monte Carlo study of the XY-model on quasi-periodic lattices

Monte Carlo Simulations were carried out using a nearest neighbour ferromagnetic XYmodel, on both 2-D and 3-D quasi-periodic lattices. In the case of 2-D, both the unfrustrated and frustrated XV-model were studied. For the unfrustrated 2-D XV-model, we have examined the magnetization, specific heat, linear susceptibility, helicity modulus and the derivative of the helicity modulus with respect to inverse temperature. The behaviour of all these quatities point to a Kosterlitz-Thouless transition occuring in temperature range Te == (1.0 -1.05) JlkB and with critical exponents that are consistent with previous results (obtained for crystalline lattices) . However, in the frustrated case, analysis of the spin glass susceptibility and EdwardsAnderson order parameter, in addition to the magnetization, specific heat and linear susceptibility, support a spin glass transition. In the case where the 'thin' rhombus is fully frustrated, a freezing transition occurs at Tf == 0.137 JlkB , which contradicts previous work suggesting the critical dimension of spin glasses to be de > 2 . In the 3-D systems, examination of the magnetization, specific heat and linear susceptibility reveal a conventional second order phase transition. Through a cumulant analysis and finite size scaling, a critical temperature of Te == (2.292 ± 0.003) JI kB and critical exponents of 0:' == 0.03 ± 0.03, f3 == 0.30 ± 0.01 and I == 1.31 ± 0.02 have been obtained.

Letter from the Secretary of War, transmitting documents containing the information required by the resolution of Mr. Wright, on the 22d inst. relative to the execution of the act fixing the military peace establishment. --

14th Congress, 1st session, 1815-1816. House. Document no. 33.

Letter from the Secretary of War, transmitting documents containing the information required by the resolution of Mr. Wright, on the 22d inst. relative to the execution of the act fixing the military peace establishment

14th Congress, 1st session, 1815-1816. House. Document no. 33. January 27, 1816. Read and referred to the Committee on Military Affairs.

Message from the President of the United States transmitting documents relative to the execution of the first article of the late treaty between the United States and Great Britain.

"February 7, 1817, ordered to be printed for the use of the Senate." Message addressed to the Senate and dated February 7th, 1817. Consists of the covering letter from the President and a report from the Secretary of State, dated Department of State, February 5th, 1817; which itself consists largely of diplomatic correspondence between the United States and Great Britain Relates to the restitution of captured slaves by the British during the War of 1812-1814.

Statement from the Sheriff’s Office, Lincoln that there are no writs of execution or extent against Owen Clifford

Statement from the Sheriff’s Office, Lincoln that there are no writs of execution or extent against Owen Clifford. This is signed by Joseph A. Woodruff, March 5, 1869.