Christopher L. Henley

Destructive quantum interference in spin tunneling problems.

In some spin tunneling problems there are several different but symmetry-related tunneling paths that connect the same initial and final configurations. The topological phase factors of the corresponding tunneling amplitudes can lead to destructive interference between the different paths, so that the total tunneling amplitude is zero. In the study of tunneling between different ground-state configurations of the kagome-lattice quantum Heisenberg antiferromagnet, this occurs when the spin s is half odd integer

Crystals and quasicrystals in the aluminum-transition metal system

Abstract Inspection of known Al-TM alloy phase diagrams and structures suggests the ideal composition and structure of the icosahedral quasicrystal phase. The phases α(AlMnSi) and α(AlFeSi) can be decomposed into packings of rhombohedra identical to those in the 3D (icosahedral) Penrose tiling, and Al 13 Fe 4 can similarly be related to the 2D Penrose tiling. Other large-cell phases can be generated by a modification of the projection method of generating Penrose tilings.

Total-energy-based prediction of a quasicrystal structure

Quasicrystals are metal alloys whose noncrystallographic symmetries challenge traditional methods of structure determination. We employ quantum-based total-energy calculations to predict the structure of a decagonal quasicrystal from first-principles considerations. Our Monte Carlo simulations take as input the knowledge that a decagonal phase occurs in Al-Ni-Co near a given composition and use a limited amount of experimental structural data. The resulting structure obeys a nearly deterministic decoration of tiles on a hierarchy of length scales related by powers of t, the golden mean.

The “Coulomb Phase” in Frustrated Systems

The “Coulomb phase” is an emergent state for lattice models (particularly highly frustrated antiferromagnets), which have local constraints that can be mapped to a divergence-free “flux.” The coarse-grained versions of this flux or polarization behave analogously to electric or magnetic fields; in particular, defects at which the local constraint is violated behave as effective charges with Coulomb interactions. I survey the derivation of the characteristic power-law correlation functions and the pinch points in reciprocal space plots of diffuse scattering, as well as applications to magnetic relaxation, quantum-mechanical generalizations, phase transitions to long-range-ordered states, and the effects of disorder.

Ordering by disorder: Ground‐state selection in fcc vector antiferromagnets

Face‐centered‐cubic antiferromagnets with vector spins (including those representing MnO and Cd1−xMnxTe) have nontrivial continuous degeneracies of their ground states which are broken by effects of either thermal or quenched disorder. Using spin‐wave calculations near T=0, it is argued that thermal fluctuations select the collinear states. On the other hand, dilution favors noncollinear (yet long‐range ordered) states.

Discussion on clusters, phasons and quasicrystal stabilisation

This paper summarises a two-hour discussion at the Ninth International Conference on Quasicrystals, including nearly 20 written comments sent afterwards, concerning (i) the meaning [if any] of clusters in quasicrystals; (ii) phason elasticity, and (iii) thermodynamic stabilisation of quasicrystals.

Relaxation time for a dimer covering with height representation

This paper considers the Monte Carlo dynamics of random dimer coverings of the square lattice, which can be mapped to a rough interface model. Two kinds of slow modes are identified, associated respectively with long-wavelength fluctuations of the interface height, and with slow drift (in time) of the system-wide mean height. Within a continuum theory, the longest relaxation time for either kind of mode scales as the system sizeN. For the real, discrete model, an exactlower bound ofO(N) is placed on the relaxation time, using variational eigenfunctions corresponding to the two kinds of continuum modes

Complex alloy phases for binary hard-disc mixtures

Abstract We investigate the phase diagram of two-dimensional binary mixtures of hard dises. There are two parameters in the problem, the ratio r of the radii of the two dises, and the concentration p of smali dises. We determine the possible phases by trying different periodic structures and minimizing the area per particle of the alloy for given r and p. We discover over ten distinct pure phases, along with large regions of the phase diagram which are oceupied by ‘lattice gas’ and ‘random tiling’ phases. The system tends to separate into two coexisting triangular lattices for r⋧ 0.5. The phase diagram becomes increasingly complicated at small size ratio and large concentrations of small discs.

Random tilings with quasicrystal order: transfer-matrix approach

The random tiling of the plane by a set of objects (e.g., rhombi), related by rotational (e.g. tenfold) symmetries, is a paradigm for the formation of quasiperiodic order due to entropy. Such tilings are mapped to a higher-dimensional space where they form hypersurfaces analogous to the interfaces in a solid-on-solid model. The author argues that the fluctuations of the hypersurface should be described by a gradient-squared free energy of entropic origin; this implies quasi-long-range order in d=2. He shows how the random tiling can be decomposed into layers, defines a transfer matrix, and give prescriptions for using this method to determine numerically the stiffness of the gradient free energy.

3D imaging and mechanical modeling of helical buckling in Medicago truncatula plant roots

We study the primary root growth of wild-type Medicago truncatula plants in heterogeneous environments using 3D time-lapse imaging. The growth medium is a transparent hydrogel consisting of a stiff lower layer and a compliant upper layer. We find that the roots deform into a helical shape just above the gel layer interface before penetrating into the lower layer. This geometry is interpreted as a combination of growth-induced mechanical buckling modulated by the growth medium and a simultaneous twisting near the root tip. We study the helical morphology as the modulus of the upper gel layer is varied and demonstrate that the size of the deformation varies with gel stiffness as expected by a mathematical model based on the theory of buckled rods. Moreover, we show that plant-to-plant variations can be accounted for by biomechanically plausible values of the model parameters.