Quantum gravity and matter: counting graphs on causal dynamical triangulations
Quantum gravity and matter: counting graphs on causal dynamical triangulations
复制标题
量子引力和物质：因果动态三角测量的计数图
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
R. Loll
中科院分区：
文献类型：
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作者：
Dario Benedetti;R. Loll
非微扰量子引力模型的一个突出挑战是在几何和物质强耦合的情况下对物理现象的一致性表述和定量评估。在开发了适当的技术工具之后，人们感兴趣的是测量和分类几何的量子涨落如何改变物质的行为，与固定背景几何相比。在二维的简化的背景下，我们展示了如何发明的方法来分析的临界行为的自旋系统的平面晶格可以适应波动的合奏弯曲时空的因果动力学三角（CDT）的方法来量子引力。我们开发了一个系统的嵌入式图形计数，以评估在高温和低温膨胀的重力物质模型的热力学函数。对于Ising模型，我们计算了CDT格点上磁化率的级数展开式及其到6阶和12阶的近似，并利用比值法、Dlog Padé和微分近似进行了分析.除了提供证据简化模型的分析结构，由于动态性质的几何形状，介绍的技术可以进一步阐明的标准à拉哈里斯和运气的影响随机几何的关键属性的物质系统。
An outstanding challenge for models of non-perturbative quantum gravity is the consistent formulation and quantitative evaluation of physical phenomena in a regime where geometry and matter are strongly coupled. After developing appropriate technical tools, one is interested in measuring and classifying how the quantum fluctuations of geometry alter the behaviour of matter, compared with that on a fixed background geometry. In the simplified context of two dimensions, we show how a method invented to analyze the critical behaviour of spin systems on flat lattices can be adapted to the fluctuating ensemble of curved spacetimes underlying the causal dynamical triangulations (CDT) approach to quantum gravity. We develop a systematic counting of embedded graphs to evaluate the thermodynamic functions of the gravity-matter models in a high- and low-temperature expansion. For the case of the Ising model, we compute the series expansions for the magnetic susceptibility on CDT lattices and their duals up to orders 6 and 12, and analyze them by ratio method, Dlog Padé and differential approximants. Apart from providing evidence for a simplification of the model’s analytic structure due to the dynamical nature of the geometry, the technique introduced can shed further light on criteria à la Harris and Luck for the influence of random geometry on the critical properties of matter systems.