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Register a new userThermal buckling transition of crystalline membranes in a field
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Two dimensional crystalline membranes in isotropic embedding space exhibit a flat phase with anomalous elasticity, relevant e.g., for graphene. Here we study their thermal fluctuations in the absence of exact rotational invariance in the embedding space. An example is provided by a membrane in an orientational field, tuned to a critical buckling point by application of in-plane stresses. Through a detailed analysis, we show that the transition is in a new universality class. The self-consistent screening method predicts a second order transition, with modified anomalous elasticity exponents at criticality, while the RG suggests a weakly first order transition.
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We revisit the universal behavior of crystalline membranes at and below the crumpling transition, which pertains to the mechanical properties of important soft and hard matter materials, such as the cytoskeleton of red blood cells or graphene. Specifically, we perform large-scale Monte Carlo simulations of a triangulated two-dimensional phantom network which is freely fluctuating in three-dimensional space. We obtain a continuous crumpling transition characterized by critical exponents which we estimate accurately through the use of finite-size techniques. By controlling the scaling corrections, we additionally compute with high accuracy the asymptotic value of the Poisson ratio in the flat phase, thus characterizing the auxetic properties of this class of systems. We obtain agreement with the value which is universally expected for polymerized membranes with a fixed connectivity.
Understanding thin sheets, ranging from the macro to the nanoscale, can allow control of mechanical properties such as deformability. Out-of-plane buckling due to in-plane compression can be a key feature in designing new materials. While thin-plate theory can predict critical buckling thresholds for thin frames and nanoribbons at very low temperatures, a unifying framework to describe the effects of thermal fluctuations on buckling at more elevated temperatures presents subtle difficulties. We develop and test a theoretical approach that includes both an in-plane compression and an out-of-plane perturbing field to describe the mechanics of thermalised ribbons above and below the buckling transition. We show that, once the elastic constants are renormalised to take into account the ribbons width (in units of the thermal length scale), we can map the physics onto a mean-field treatment of buckling, provided the length is short compared to a ribbon persistence length. Our theoretical predictions are checked by extensive molecular dynamics simulations of thin thermalised ribbons under axial compression.
We investigate the thermodynamic properties and the lattice stability of two-dimensional crystalline membranes, such as graphene and related compounds, in the low temperature quantum regime $Trightarrow0$. A key role is played by the anharmonic coupling between in-plane and out-of plane lattice modes that, in the quantum limit, has very different consequences than in the classical regime. The role of retardation, namely of the frequency dependence, in the effective anharmonic interactions turns out to be crucial in the quantum regime. We identify a crossover temperature, $T^{*}$, between classical and quantum regimes, which is $sim 70 - 90$ K for graphene. Below $T^{*}$, the heat capacity and thermal expansion coefficient decrease as power laws with decreasing temperature, tending to zero for $Trightarrow0$ as required by the third law of thermodynamics.
We study many-body chaos in a (2+1)D relativistic scalar field theory at high temperatures in the classical statistical approximation, which captures the quantum critical regime and the thermal phase transition from an ordered to a disordered phase. We evaluate out-of-time ordered correlation functions (OTOCs) and find that the associated Lyapunov exponent increases linearly with temperature in the quantum critical regime, and approaches the non-interacting limit algebraically in terms of a fluctuation parameter. OTOCs spread ballistically in all regimes, also at the thermal phase transition, where the butterfly velocity is maximal. Our work contributes to the understanding of the relation between quantum and classical many-body chaos and our method can be applied to other field theories dominated by classical modes at long wavelengths.
The magnetic properties and phase diagrams of the mixed spin Ising model, with spins S=1 and {sigma}=1/2 on a centered rectangular structure, have been investigated using Monte Carlo simulations based on the Metropolis algorithm. Every spin at one lattice site has four nearest-neighbor spins of the same type and four of the other type. We have assumed ferromagnetic interaction between the same spins type, antiferromagnetic for different spin types. An additional single-site crystal field term on the S=1 site was considered. We have shown that the crystal field enhances the existence of the compensation behavior of the system. In addition, the effects of the crystal field and exchange coupling on the magnetic properties and phase diagrams of the system have been studied. Finally, the magnetic hysteresis cycles of the system for several values of the crystal field have been found.
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