在基礎的相變理論當中，由Paul-Ehrenfest提出的方法來對相變進行分類，將相
變分為一階相變或者二階相變，主要的差別取決於熱力學自由能隨著溫度的改變，
是否連續以及是否具有潛熱。通過加熱鐵磁體使其溫度高於居禮溫度的方式破壞磁
性長程有序，就是一種二階相變，此時相變的調變參數為溫度，熱擾動為此二階相
變發生的主要因素並且主宰了相變點附近的物理性質。如果我們可以藉由與溫度無
關的調變參數，將這種二階相變的相變溫度降到絕對零度，此時量子擾動主宰了
相變點附近的物理行為，這種相變被稱為量子二階相變，而此時的相變點又被稱
為量子臨界點。早期由Hertz, Millis, 與Moriya三人提出的量子相變理論，描述了磁
性量子臨界點可以存在鐵磁性或反鐵磁性的系統中，然而實驗上很難觀測到鐵磁
量子臨界點的出現。後來Belitz, Kirkpatrick, 和Vojta (BKV)三人解釋了為何會產生
這樣的結果，並進一步預測鐵磁性金屬能夠透過調變化學失序使相變溫度下降，
進而產生鐵磁量子臨界點。我們已經在先前的研究發現，鎳銠合金(Ni1-xRhx)的臨
界溫度隨著非磁性銠金屬的摻雜(化學失序)比例上升而下降，最終在摻雜比例達
到x = 0.375時(此比例被稱為量子臨界濃度)，居禮溫度下降至絕對零度，比熱與
熱膨脹係數在低溫存在發散的情形，這是量子臨界現象發生的明顯證據。在這篇
碩士論文中，我採用處於量子臨界濃度的鎳銠合金數據，來進行超標度分析以驗
證BKV理論中對臨界指數的預測數值，得到的動態臨界指數顯示x = 0.375離真正的
量子臨界濃度還存在一小段距離，這說明這個系統並不是精準地處於量子臨界點之
上，此發現和BKV理論描述吻合，證明化學失序確實可以用來調變產生鐵磁量子臨
界點。

A fundamental theory of phase transitions presented by Paul-Ehrenfeset is used to distinguish first-order and second-order phase transitions. The main difference between the two is whether the thermodynamic free energy changes continuously as altering temperature, and whether the transition involves latent heat. For example, a ferromagnetic transition between long-range order and disorder as varying the temperature across the Curie temperature is a second-order phase transition. Here, the temperature is a tuning parameter and thermal fluctuations destroys the magnetic order. We could suppress the second-order phase transition temperature to absolute zero by non-thermal tuning parameters and reach a quantum phase transition where the quantum fluctuations destroy the order and dominate physical properties. At the early stage, Hertz, Millis and Moriya supposed the quantum critical point (QCP) can be found both in a ferromagnet and an antiferromagnet, but the experimental evidence shows the QCP in a ferromagnet is scarce. Later, Belitz, Kirkpatrick and Vojta(BKV) explained what causes such a fact, and further predicted the ferromagnetic(FM) QCP could be reached by introducing chemical disorder. Our previous work[1] shows the Curie temperature in Ni1-xRhx alloys decreases as the Rh concentration increases and reaches absolute zero when x = 0.375. Both the specific heat and thermal expansion coefficients diverge as decreasing temperature, providing evidence of a FM QCP. In this thesis, I did the hyperscaling analysis of Ni$_{1-x}$Rh$_{x}$ with $x = 0.375$ and determined dynamical critical exponents $z$. The $z$ value shows that there is finite distance to the true QCP for $x = 0.375$ in Ni$_{1-x}$Rh$_{x}$. Nevertheless, our result reinforces the role of chemical disorder to tune the FM QCP, as proposed by the BKV theory.

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