Absence of phase transitions in one-dimensional long-range spin systems with random Hamiltonian

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 $\alpha>3/2$.