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 acting Secretary of War, transmitting information relative to the claims of the State of Massachusetts for payment of the expenses of the militia ordered out by the executive authority of the state, during the late war. --

15th Congress, 1st session, 1817-1818, House. Doc. 81.

Message from the President of the United States, in relation to the claim of Virginia, an account of interest paid by that State, on moneys borrowed for the payment of the militia thereof, for services rendered the United States.--

April 13, 1824. Printed by order of the Senate of the United States.

Letter from the acting Secretary of War, transmitting information relative to the claims of the State of Massachusetts for payment of the expenses of the militia ordered out by the executive authority of the state, during the late war

15th Congress, 1st session, 1817-1818, House. Doc. 81. February 20, 1817. Read, and ordered to lie upon the table.

Message from the President of the United States, in relation to the claim of Virginia, an account of interest paid by that State, on moneys borrowed for the payment of the militia thereof, for services rendered the United States

April 13, 1824. Printed by order of the Senate of the United States. At head of title: 18th congress, 1st session. [64]. Printed by Cales and Seaton

Payment for Property - War of 1812-14 (1824)

Government report in congress discussing payment for property during the War of 1812.

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