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Teoreticheskaya i Matematicheskaya Fizika, 1980, Volume 43, Number 2, Pages 253–260
(Mi tmf3219)
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This article is cited in 20 scientific papers (total in 20 papers)
Absence of phase transitions in one-dimensional long-range spin systems with random Hamiltonian
K. M. Khanin
Abstract:
Classical lattice one-dimensional systems with random Hamiltonians
$H=\dfrac\beta2\sum\limits_{x_1\ne x_2}\dfrac{\varepsilon(x_1,x_2)\varphi(x_1)\varphi(x_2)}{|x_1-x_2|^\alpha}$
are considered, where $\varepsilon(x_1,x_2)$ are independent random variables for different pairs $(x_1,x_2)$, $E\varepsilon(x_1,x_2)=0$. It is shown that with probability 1 such a system has no phase transition, provided $\alpha>3/2$.
Received: 31.01.1979
Citation:
K. M. Khanin, “Absence of phase transitions in one-dimensional long-range spin systems with random Hamiltonian”, TMF, 43:2 (1980), 253–260; Theoret. and Math. Phys., 43:2 (1980), 445–449
Linking options:
https://www.mathnet.ru/eng/tmf3219 https://www.mathnet.ru/eng/tmf/v43/i2/p253
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